Numerical methods for large-scale nonlinear optimization

Acta Numerica

Volumn 14, Issue , 2005, Pages 299-361

  Gould, Nick ^a   Orban, Dominique ^b   Toint, Philippe ^c  

^a RUTHERFORD APPLETON LABORATORY   (United Kingdom)

^b ÉCOLE POLYTECHNIQUE DE MONTRÉAL   (Canada)

^c UNIVERSITY OF NAMUR   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 19844363263     PISSN: 09624929     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0962492904000248     Document Type: Review

References (257)

1. M. Al-Baali (2003), Quasi-Newton algorithms for large-scale nonlinear least-squares, in Di Pillo and Murli (2003), pp. 1-21.
2. E. D. Andersen and K. D. Andersen (2000), The MOSEK interior point optimizer for linear programming: An implementation of the homogeneous algorithm, in High Performance Optimization (T. T. H. Frenk, K. Roos and S. Zhang, eds), Kluwer, pp. 197-232.
3. E. D. Andersen and Y. Ye (1998), 'A computational study of the homogeneous algorithm for large-scale convex optimization', Comput. Optim. Appl. 10, 243-269.
4. E. D. Andersen and Y. Ye (1999), 'On a homogeneous algorithm for the monotone complementarity problem', Math. Program. 84(2), 375-399.
5. M. Anitescu (2000), On using the elastic mode in nonlinear programming approaches to mathematical programs with complementarity constraints, Preprint ANL/MCS-P864-1200, Argonne National Laboratory, IL, USA.
6. E. Arian, M. Fahl and E. W. Sachs (2000), Trust-region proper orthogonal decomposition for flow control, Technical Report 2000-25, Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, Hampton, VA, USA.
7. A. S. El Bakry, R. A. Tapia, T. Tsuchiya and Y. Zhang (1996), 'On the formulation and theory of Newton interior point methods for nonlinear programming', J. Optim. Theory Appl. 89(3), 507-541.
8. R. E. Bank, P. E. Gill and R. F. Marcia (2003), Interior point methods for a class of elliptic variational inequalities, in Biegler, Ghattas, Heinkenschloss and Van Bloemen Waanders (2003), pp. 218-235.
9. H. Y. Benson, A. Sen, D. F. Shanno and R. J. Vanderbei (2003), Interior-point algorithms, penalty methods and equilibrium problems, Technical Report ORFE-03-02, Operations Research and Financial Engineering, Princeton University.
10. H. Y. Benson, R. J. Vanderbei and D. F. Shanno (2002), 'Interior-point methods for nonconvex nonlinear programming: Filter methods and merit functions', Comput. Optim. Appl. 23, 257-272.
11. S. J. Benson, L. C. McInnes, J. More and J. Sarich (2004), Scalable algorithms in optimization: Computational experiments, Preprint ANL/MCS-P1175-0604, Mathematics and Computer Science, Argonne National Laboratory, Argonne, IL, USA. To appear in Proc. 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization (MA&O) Conference, August 30-September 1, 2004.
12. D. P. Bertsekas (1976), 'On the Goldstein-Levitin-Poljak gradient projection method', IEEE Trans. Automat. Control AC-21, 174-184.
13. D. P. Bertsekas (1995), Nonlinear Programming, Athena Scientific, Belmont, MA, USA.
14. J. T. Betts and S. O. Erb (2003), 'Optimal low thrust trajectory to the moon', SIAM J. Appl. Dyn. Syst. 2(2), 144-170.
15. J. T. Betts and P. D. Frank (1994), 'A sparse nonlinear optimization algorithm', J. Optim. Theory Appl. 82(3), 519-541.
16. T. Biegler, O. Ghattas, M. Heinkenschloss and B. Van Bloemen Waanders, eds (2003), High Performance Algorithms and Software for Nonlinear Optimization, Springer, Heidelberg/Berlin/New York.
17. G. Biros and O. Ghattas (2000), 'A Lagrange-Newton-Krylov-Schur method for PDE-constrained optimization', SIAG/OPT Views-and-News 11(2), 12-18.
18. R. E. Bixby, M. Fenlon, Z. Gu, E. Rothberg and R. Wunderling (2000), MIP: theory and practice; closing the gap, in System Modelling and Optimization: Methods, Theory and Applications (M. J. D. Powell and S. Scholtes, eds), Kluwer, Dordrecht, Netherlands, pp. 10-49.
19. P. T. Boggs and J. W. Tolle (1995), Sequential quadratic programming, in Acta Numerica, Vol. 4, Cambridge University Press, pp. 1-51.
20. P. T. Boggs and J. W. Tolle (2000), 'Sequential quadratic programming for large-scale nonlinear optimization', Comput. Appl. Math. 124, 123-137.
21. P. T. Boggs, P. D. Domich, J. E. Rogers and C. Witzgall (1996), 'An interior point method for general large scale quadratic programming problems', Ann. Oper. Res. 62, 419-437.
22. P. T. Boggs, A. J. Kearsley and J. W. Tolle (1999a), 'A global convergence analysis of an algorithm for large scale nonlinear programming problems', SIAM J. Optim. 9(4), 833-862.
23. P. T. Boggs, A. J. Kearsley and J. W. Tolle (1999b), 'A practical algorithm for general large scale nonlinear optimization problems', SIAM J. Optim. 9(3), 755-778.
24. J. F. Bonnans, J.-Ch. Gilbert, C. Lemaréchal and C. Sagastizábal (1997), Optimisation Numérique: Aspects Théoriques et Pratiques, Vol. 27 of Mathématiques & Applications, Springer.
25. J. M. Borwein (1982), 'Necessary and sufficient conditions for quadratic minimality', Numer. Funct. Anal. Optim. 5, 127-140.
26. J. H. Bramble (1993), Multigrid Methods, Longman, New York.
27. M. A. Branch, T. F. Coleman and Y. Li (1999), 'A subspace, interior and conjugate gradient method for large-scale bound-constrained minimization problems', SIAM J. Sci. Comput. 21(1), 1-23.
28. A. Brandt (1977), 'Multi-level adaptative solutions to boundary value problems', Math. Comp. 31(138), 333-390.
29. W. L. Briggs, V. E. Henson and S. F. McCormick (2000), A Multigrid Tutorial, second edn, SIAM, Philadelphia, USA.
30. A. Brooke, D. Kendrick and A. Meeraus (1988), GAMS: A User's Guide, The Scientific Press, Redwood City, USA.
31. J. V. Burke and J. J. More (1988), 'On the identification of active constraints', SIAM J. Numer. Anal. 25(5), 1197-1211.
32. J. V. Burke and J. J. More (1994), 'Exposing constraints', SIAM J. Optim. 4(3), 573-595.
33. J. V. Burke and A. Weigmann (1997), Notes on limited memory BFGS updating in a trust-region framework, Technical report, Department of Mathematics, University of Washington, Seattle, Washington, USA.
34. J. V. Burke, J. J. Moré and G. Toraldo (1990), 'Convergence properties of trust region methods for linear and convex constraints', Math. Program. 47(3), 305-336.
35. R. H. Byrd, J.-Ch. Gilbert and J. Nocedal (2000), 'A trust region method based on interior point techniques for nonlinear programming', Math. Program., Ser. A 89(1), 149-185.
36. R. H. Byrd, N. I. M. Gould, J. Nocedal and R. A. Waltz (2004a), 'An algorithm for nonlinear optimization using linear programming and equality constrained subproblems', Math. Program., Ser. B 100(1), 27-48.
37. R. H. Byrd, N. I. M. Gould, J. Nocedal and R. A. Waltz (2004b), On the convergence of successive linear-quadratic programming algorithms, Technical Report RAL-TR-2004-032, Rutherford Appleton Laboratory, Chilton, Oxfordshire, UK.
38. R. H. Byrd, M. E. Hribar and J. Nocedal (1999), 'An interior point method for large scale nonlinear programming', SIAM J. Optim. 9(4), 877-900.
39. R. H. Byrd, P. Lu, J. Nocedal and C. Zhu (1995), 'A limited memory algorithm for bound constrained optimization', SIAM J. Sci. Comput. 16(5), 1190-1208.
40. R. H. Byrd, J. Nocedal and R. B. Schnabel (1994), 'Representations of quasi-Newton matrices and their use in limited memory methods', Math. Program. 63(2), 129-156.
41. R. H. Byrd, J. Nocedal and R. A. Waltz (2003), 'Feasible interior methods using slacks for nonlinear optimization', Comput. Optim. Appl. 26, 35-61.
42. P. H. Calamai and J. J. More (1987), 'Projected gradient methods for linearly constrained problems', Math. Program. 39(1), 93-116.
43. Y. Chabrillac and J.-P. Crouzeix (1984), 'Definiteness and semidefiniteness of quadratic forms revisited', Linear Algebra Appl. 63, 283-292.
44. C. M. Chin and R. Fletcher (2003), 'On the global convergence of an SLP-filter algorithm that takes EQP steps', Math. Program. 96(1), 161-177.
45. T. F. Coleman (1994), Linearly constrained optimization and projected preconditioned conjugate gradients, in Proc. Fifth SIAM Conference on Applied Linear Algebra (J. Lewis, ed.), SIAM, Philadelphia, USA, pp. 118-122.
46. T. F. Coleman and A. R. Conn (1982), 'Nonlinear programming via an exact penalty function method: Asymptotic analysis', Math. Program. 24(3), 123-136.
47. T. F. Coleman and L. A. Hulbert (1989), 'A direct active set algorithm for large sparse quadratic programs with simple bounds', Math. Program., Ser. B 45(3), 373-406.
48. T. F. Coleman and Y. Li, eds (1990), Large Scale Numerical Optimization, SIAM, Philadelphia, USA.
49. T. F. Coleman and Y. Li (1994), 'On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds', Math. Program. 67(2), 189-224.
50. T. F. Coleman and Y. Li (1996), 'An interior trust region approach for nonlinear minimization subject to bounds', SIAM J. Optim. 6(2), 418-445.
51. T. F. Coleman and Y. Li (2000), 'A trust region and affine scaling interior point method for nonconvex minimization with linear inequality constraints', Math. Program., Ser. A 88, 1-31.
52. B. Colson and Ph. L. Toint (2003), Optimizing partially separable functions without derivatives, Technical Report 03/20, Department of Mathematics, University of Namur, Namur, Belgium.
53. A. R. Conn, N. I. M. Gould and Ph. L. Toint (1988a), 'Global convergence of a class of trust region algorithms for optimization with simple bounds', SIAM J. Numer. Anal 25(2), 433-460. See also same journal 26 (1989), 764-767.
54. A. R. Conn, N. I. M. Gould and Ph. L. Toint (1988b), 'Testing a class of methods for solving minimization problems with simple bounds on the variables', Math. Comp. 50, 399-430.
55. A. R. Conn, N. I. M. Gould and Ph. L. Toint (1990), An introduction to the structure of large scale nonlinear optimization problems and the LANCELOT project, in Computing Methods in Applied Sciences and Engineering (R. Glowinski and A. Lichnewsky, eds), SIAM, Philadelphia, USA, pp. 42-51.
56. A. R. Conn, N. I. M. Gould and Ph. L. Toint (1992), LANCELOT; A Fortran package for Large-scale Nonlinear Optimization (Release A), Springer Series in Computational Mathematics, Springer, Heidelberg/Berlin/New York.
57. A. R. Conn, N. I. M. Gould and Ph. L. Toint (1994), Large-scale nonlinear constrained optimization: a current survey, in Algorithms for Continuous Optimization: The State of the Art (E. Spedicato, ed.), Vol. 434 of NATO ASI Series C: Mathematical and Physical Sciences, Kluwer, Dordrecht, Netherlands, pp. 287-332.
58. A. R. Conn, N. I. M. Gould and Ph. L. Toint (1996), 'Numerical experiments with the LANCELOT package (Release A) for large-scale nonlinear optimization', Math. Program., Ser. A 73(1), 73-110.
59. A. R. Conn, N. I. M. Gould and Ph. L. Toint (1997), Methods for nonlinear constraints in optimization calculations, in Duff and Watson (1997), pp. 363-390.
60. A. R. Conn, N. I. M. Gould and Ph. L. Toint (2000a), Trust-Region Methods, SIAM, Philadelphia, USA.
61. A. R. Conn, N. I. M. Gould, D. Orban and Ph. L. Toint (2000b), 'A primal-dual trust-region algorithm for non-convex nonlinear programming', Math. Program., Ser. B 87(2), 215-249.
62. B. L. Contesse (1980), 'Une caractérisation complète des minima locaux en programmation quadratique', Numer. Math. 34(3), 315-332.
63. CPLEX 6.0 (1998), High-Performance Linear, Integer and Quadratic Programming Software, ILOG SA, Gentilly, France, www.cplex.com.
64. J. Czyzyk, M. Mesnier and J. More (1998), 'The NEOS server', IEEE J. Comput. Sci. Engr. 5, 68-75.
65. Y. H. Dai and Y. Yuan (2000), 'A nonlinear conjugate gradient method with a strong global convergence property', SIAM J. Optim. 10(1), 177-182.
66. R. S. Dembo and T. Steihaug (1983), 'Truncated-Newton algorithms for large-scale unconstrained optimization', Math. Program. 26(2), 190-212.
67. R. S. Dembo, S. C. Eisenstat and T. Steihaug (1982), 'Inexact-Newton methods', SIAM J. Numer. Anal. 19(2), 400-408.
68. A.-V. DeMiguel, M. P. Friedlander, F. J. Nogales and S. Scholtes (2004), An interior-point method for MPECs based on strictly feasible relaxations, Technical Report ANL/MCS-P1150-0404, Argonne National Laboratory, IL, USA.
69. N. Deng, Y. Xiao and F. Zhou (1993), 'Nonmonotonic trust region algorithms', J. Optim. Theory Appl. 76(2), 259-285.
70. J. E. Dennis and R. B. Schnabel (1983), Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, USA.
71. Reprinted as Vol. 16 of Classics in Applied Mathematics, SIAM, Philadelphia, USA.
72. J. E. Dennis, D. M. Gay and R. E. Welsh (1981), 'An adaptive nonlinear least squares algorithm', ACM Trans. Math. Software 7(3), 348-368.
73. G. Di Pillo and F. Gianessi, eds (1996), Nonlinear Optimization and Applications, Plenum Publishing, New York.
74. G. Di Pillo and F. Gianessi, eds (1999), Nonlinear Optimization and Related Topics, Vol. 2, Kluwer, Dordrecht, Netherlands.
75. G. Di Pillo and A. Murli, eds (2003), High Performance Algorithms and Software in Nonlinear Optimization, Kluwer, Dordrecht, Netherlands.
76. E. Dolan (2001), The NEOS server 4.0 administrative guide, Technical Memorandum ANL/MCS-TM-250, Argonne National Laboratory, IL.
77. E. D. Dolan, R. Fourer, J. J. Moŕe and T. S. Munson (2002), 'Computing a trust region step', SIAM News 35(5), 8-9.
78. A. S. Drud (1994), 'CONOPT: A large scale GRG code', ORSA J. Comput. 6, 207-216.
79. I. Duff and A. Watson, eds (1997), The State of the Art in Numerical Analysis, Oxford University Press, Oxford.
80. J. C. Dunn (1981), 'Global and asymptotic convergence rate estimates for a class of projected gradient processes', SIAM J. Control Optim. 19, 368-400.
81. J.-P. Dussault (1995), 'Numerical stability and efficiency of penalty algorithms', SIAM J. Numer. Anal. 32(1), 296-317.
82. O. Epelly, J. Gondzio and J.-P. Vial (2000), An interior-point solver for smooth convex optimization with an application to environmental-energy-economic models, Technical Report 2000.08, Logilab, HEC, University of Geneva, Switzerland.
83. F. Facchinei, J. Judice and J. Soares (1998), 'An active set Newton algorithm for large-scale nonlinear programs with box constraints', SIAM J. Optim. 8(1), 158-186.
84. F. Facchinei, S. Lucidi and L. Palagi (2002), 'A truncated Newton algorithm for large scale box constrained optimization', SIAM J. Optim. 12(4), 1100-1125.
85. M. Fahl and E. Sachs (2003), Reduced order modelling approaches to PDE-constrained optimization based on proper orthogonal decomposition, in Biegler et al. (2003), pp. 268-281.
86. M. C. Ferris and T. S. Munson (2000), Interior-point methods for massive support vector machines, Data Mining Institute Technical Report 00-05, Computer Science Department, University of Wisconsin, Madison, WI, USA.
87. A. V. Fiacco and G. P. McCormick (1968), Nonlinear Programming: Sequential Unconstrained Minimization Techniques, Wiley, Chichester, UK.
88. Reprinted as Classics in Applied Mathematics, SIAM, Philadelphia, USA (1990).
89. M. Fisher (1998), Minimization algorithms for variational data assimilation, in Recent Developments in Numerical Methods for Atmospheric Modelling, ECMWF, pp. 364-385.
90. R. Fletcher (1971), 'A general quadratic programming algorithm', J. Inst. Math. Appl. 7, 76-91.
91. R. Fletcher (1981), Practical Methods of Optimization: Constrained Optimization, Wiley, Chichester, UK.
92. R. Fletcher (1987a), Practical Methods of Optimization, second edn, Wiley, Chichester, UK.
93. R. Fletcher (1987b), Recent developments in linear and quadratic programming, in The State of the Art in Numerical Analysis (A. Iserles and M. J. D. Powell, eds), Oxford University Press, Oxford, pp. 213-243.
94. R. Fletcher (2000), 'Stable reduced Hessian updates for indefinite quadratic programming', Math. Program. 87(2), 251-264.
95. R. Fletcher and S. Leyffer (1998), User manual for filterSQP, Numerical Analysis Report NA/181, Department of Mathematics, University of Dundee, Dundee, UK.
96. R. Fletcher and S. Leyffer (2002), 'Nonlinear programming without a penalty function', Math. Program. 91(2), 239-269.
97. R. Fletcher and C. M. Reeves (1964), 'Function minimization by conjugate gradients', Computer Journal 7, 149-154.
98. R. Fletcher and E. Sainz de la Maza (1989), 'Nonlinear programming and nonsmooth optimization by successive linear programming', Math. Program. 43(3), 235-256.
99. R. Fletcher, N. I. M. Gould, S. Leyffer, Ph. L. Toint and A. Wächter (2002a), 'Global convergence of trust-region SQP-filter algorithms for nonlinear programming', SIAM J. Optim. 13(3), 635-659.
100. R. Fletcher, S. Leyffer and Ph. L. Toint (2002b), 'On the global convergence of a filter-SQP algorithm', SIAM J. Optim. 13(1), 44-59.
101. A. Forsgren (2002), 'Inertia-controlling factorizations for optimization algorithms', Appl. Numer. Math. 43(1-2), 91-107.
102. A. Forsgren and P. E. Gill (1998), 'Primal-dual interior methods for nonconvex nonlinear programming', SIAM J. Optim. 8(4), 1132-1152.
103. A. Forsgren and W. Murray (1993), 'Newton methods for large-scale linear equality-constrained minimization', SIAM J. Matrix Anal. Appl. 14(2), 560-587.
104. A. Forsgren, P. E. Gill and M. H. Wright (2002), 'Interior-point methods for nonlinear optimization', SIAM Review 44, 525-597.
105. R. Fourer, D. M. Gay and B. W. Kernighan (2003), AMPL: A Modeling Language for Mathematical Programming, second edn, Brooks/Cole-Thompson Learning, Pacific Grove, CA, USA.
106. M. P. Friedlander and M. A. Saunders (2005), 'A globally convergent linearly constrained Lagrangian method for nonlinear optimization', SIAM J. Optim., to appear.
107. D. M. Gay, M. L. Overton and M. H. Wright (1998), A primal-dual interior method for nonconvex nonlinear programming, in Advances in Nonlinear Programming (Y. Yuan, ed.), Kluwer, Dordrecht, Netherlands, pp. 31-56.
108. E. M. Gertz and Ph. E. Gill (2004), 'A primal-dual trust region algorithm for nonlinear optimization', Math. Program., Ser. A 100(1), 49-94.
109. E. M. Gertz and S. J. Wright (2003), 'Object-oriented software for quadratic programming', Trans. ACM Math. Software 29(1), 58-81.
110. E. M. Gertz, J. Nocedal and A. Sartenaer (2003), A starting-point strategy for nonlinear interior methods, Technical Report OTC 2003/4, Optimization Technology Center, Evanston, IL, USA.
111. J.-Ch. Gilbert and C. Lemaréchal (1989), 'Some numerical experiments with variable-storage quasi-Newton algorithms', Math. Program., Ser. B 45(3), 407-435.
112. J.-Ch. Gilbert and J. Nocedal (1992), 'Global convergence properties of conjugate gradient methods for optimization', SIAM J. Optim. 2(1), 21-42.
113. J.-Ch. Gilbert, C. C. Gonzaga and E. Karas (2002), Examples of ill-behaved central paths in convex optimization, Technical Report 4179, INRIA, Rocquencourt, Le Chesnay, France.
114. P. E. Gill, W. Murray and M. A. Saunders (2002), 'SNOPT: An SQP algorithm for large-scale constrained optimization', SIAM J. Optim. 12(4), 979-1006.
115. P. E. Gill, W. Murray and M. H. Wright (1981), Practical Optimization, Academic Press, London.
116. P. E. Gill, W. Murray, M. A. Saunders and M. H. Wright (1990), A Schur-complement method for sparse quadratic programming, in Reliable Scientific Computation (M. G. Cox and S. J. Hammarling, eds), Oxford University Press, pp. 113-138.
117. P. E. Gill, W. Murray, M. A. Saunders and M. H. Wright (1991), 'Inertia-controlling methods for general quadratic programming', SIAM Review 33(1), 1-36.
118. M. J. Goldsmith (1999), Sequential quadratic programming methods based on indefinite Hessian approximations, PhD thesis, Dept of Management Science and Engineering, Stanford University, CA, USA.
119. J. Gondzio (1996), 'Multiple centrality corrections in a primal-dual method for linear programming', Comput. Optim. Appl. 6, 137-156.
120. J. Gondzio (1997), 'Presolve analysis of linear programs prior to applying an interior point method', INFORMS J. Comput. 9(1), 73-91.
121. J. Gondzio and A. Grothey (2003a), Parallel interior point solver for structured quadratic programs: Application to financial planning problems, Technical Report MS-03-001, School of Mathematics, University of Edinburgh.
122. J. Gondzio and A. Grothey (2003b), 'Reoptimization with the primal-dual interior point method', SIAM J. Optim. 13(3), 842-864.
123. C. C. Gonzaga, E. Karas and M. Vanti (2003), 'A globally convergent filter method for nonlinear programming', SIAM J. Optim. 14(3), 646-669.
124. N. I. M. Gould (1985), 'On practical conditions for the existence and uniqueness of solutions to the general equality quadratic-programming problem', Math. Program. 32(1), 90-99.
125. N. I. M. Gould (1986), 'On the accurate determination of search directions for simple differentiable penalty functions', IMA J. Numer. Anal. 6, 357-372.
126. N. I. M. Gould (1991), 'An algorithm for large-scale quadratic programming', IMA J. Numer. Anal. 11(3), 299-324.
127. N. I. M. Gould (1999), 'On modified factorizations for large-scale linearly-constrained optimization', SIAM J. Optim. 9(4), 1041-1063.
128. N. I. M. Gould (2003), 'Some reflections on the current state of active-set and interior point methods for constrained optimization', SIAG/OPT Views-and-News 14(1), 2-7.
129. N. I. M. Gould, and Ph. L. Toint (2000a), A quadratic programming bibliography, Numerical Analysis Group Internal Report 2000-1, Rutherford Appleton Laboratory, Chilton, Oxfordshire, UK.
130. N. I. M. Gould and Ph. L. Toint (2000b), SQP methods for large-scale nonlinear programming, in System Modelling and Optimization: Methods, Theory and Applications (M. J. D. Powell and S. Scholtes, eds), Kluwer, Dordrecht, Netherlands, pp. 149-178.
131. N. I. M. Gould and Ph. L. Toint (2002a), 'An iterative working-set method for large-scale non-convex quadratic programming', Appl. Numer. Math. 43(1-2), 109-128.
132. N. I. M. Gould and Ph. L. Toint (2002b), Numerical methods for large-scale non-convex quadratic programming, in Trends in Industrial and Applied Mathematics (A. H. Siddiqi and M. Kočvara, eds), Kluwer, Dordrecht, Netherlands, pp. 149-179.
133. N. I. M. Gould and Ph. L. Toint (2003a), FILTRANE: A Fortran 95 filter-trust-region package for solving systems of nonlinear equalities, nonlinear inequalities and nonlinear least-squares problems, Technical Report 03/15, Rutherford Appleton Laboratory, Chilton, Oxfordshire, UK.
134. N. I. M. Gould and Ph. L. Toint (2003b), Global convergence of a hybrid trust-region SQP-filter algorithm for general nonlinear programming, in System Modeling and Optimization XX (E. Sachs and R. Tichatschke, eds), Kluwer, Dordrecht, Netherlands, pp. 23-54.
135. N. I. M. Gould and Ph. L. Toint (2004a), How mature is nonlinear optimization?, in Applied Mathematics Entering the 21st Century: Invited Talks from the ICIAM 2003 Congress (J. M. Hill and R. Moore, eds), SIAM, Philadelphia, USA, pp. 141-161.
136. N. I. M. Gould and Ph. L. Toint (2004b), 'Preprocessing for quadratic programming', Math. Program., Ser. B 100(1), 95-132.
137. N. I. M. Gould and Ph. L. Toint (2005), Global convergence of a non-monotone trust-region filter algorithm for nonlinear programming, in Proc. 2004 Gainesville Conference on Multilevel Optimization (W. Hager, ed.), Kluwer, Dordrecht, Netherlands, to appear.
138. N. I. M. Gould, M. E. Hribar and J. Nocedal (2001), 'On the solution of equality constrained quadratic problems arising in optimization', SIAM J. Sci. Comput. 23(4), 1375-1394.
139. N. I. M. Gould, S. Leyffer and Ph. L. Toint (2005), 'A multidimensional filter algorithm for nonlinear equations and nonlinear least-squares', SIAM J. Optim. 15(1), 17-38.
140. N. I. M. Gould, S. Lucidi, M. Roma and Ph. L. Toint (1999), 'Solving the trust-region subproblem using the Lanczos method', SIAM J. Optim. 9(2), 504-525.
141. N. I. M. Gould, S. Lucidi, M. Roma and Ph. L. Toint (2000), 'Exploiting negative curvature directions in linesearch methods for unconstrained optimization', Optim. Methods Software 14(1-2), 75-98.
142. N. I. M. Gould, D. Orban and Ph. L. Toint (2003a), 'GALAHAD: A library of thread-safe Fortran 90 packages for large-scale nonlinear optimization', ACM Trans. Math. Software 29(4), 353-372.
143. 1-penalty method for nonlinear optimization, Technical Report RAL-TR-2003-0xx, Rutherford Appleton Laboratory, Chilton, Oxfordshire, UK.
144. N. I. M. Gould, C. Sainvitu and Ph. L. Toint (2004), A filter-trust-region method for unconstrained optimization, Technical Report 04/03, Department of Mathematics, University of Namur, Belgium.
145. S. Gratton, A. Sartenaer and Ph. L. Toint (2004), Recursive trust-region methods for multilevel nonlinear optimization (Part I): Global convergence and complexity, Technical Report 04/06, Department of Mathematics, University of Namur, Belgium.
146. A. Griewank (2000), Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, Vol. 19 of Frontiers in Applied Mathematics, SIAM, Philadelphia, USA.
147. A. Griewank and Ph. L. Toint (1982a), 'Local convergence analysis for partitioned quasi-Newton updates', Numer. Math. 39, 429-448.
148. A. Griewank and Ph. L. Toint (1982b), On the unconstrained optimization of partially separable functions, in Nonlinear Optimization 1981 (M. J. D. Powell, ed.), Academic Press, London, pp. 301-312.
149. A. Griewank and Ph. L. Toint (1982c), 'Partitioned variable metric updates for large structured optimization problems', Numer. Math. 39, 119-137.
150. R. E. Griffith and R. A. Stewart (1961), 'A nonlinear programming technique for the optimization of continuous processing systems', Management Science 7, 379-392.
151. L. Grippo, F. Lampariello and S. Lucidi (1986), 'A nonmonotone line search technique for Newton's method', SIAM J. Numer. Anal. 23(4), 707-716.
152. L. Grippo, F. Lampariello and S. Lucidi (1989), 'A truncated Newton method with nonmonotone line search for unconstrained optimization', J. Optim. Theory Appl. 60(3), 401-419.
153. W. Gropp and J. More (1997), Optimization environments and the NEOS server, in Approximation Theory and Optimization (M. D. Buhmann and A. Iserles, eds), Cambridge University Press, pp. 167-182.
154. C. Guér C. Prins and M. Seveaux (2002), Applications of Optimization with Xpress-MP, Dash Optimization, www.dashoptimization.com.
155. M. Gulliksson, I. Söderkvist and P.-A. Wedin (1997), 'Algorithms for constrained and weighted nonlinear least-squares', SIAM J. Optim. 7(1), 208-224.
156. W. Hackbusch (1995), Multi-Grid Methods and Applications, Vol. 4 of Series in Computational Mathematics, Springer, Heidelberg/Berlin/New York.
157. W. W. Hager (2001), 'Minimizing a quadratic over a sphere', SIAM J. Optim. 12(1), 188-208.
158. W. W. Hager and H. Zhang (2003), CG DESCENT: A conjugate-gradient method with guaranteed descent, Technical report, Department of Mathematics, University of Florida, Gainesville, USA.
159. W. W. Hager, D. W. Hearn and P. M. Pardalos, eds (1994), Large Scale Optimization: State of the Art, Kluwer, Dordrecht, Netherlands.
160. M. Heinkenschloss, M. Ulbrich and S. Ulbrich (1999), 'Superlinear and quadratic convergence of affine-scaling interior-point Newton methods for problems with simple bounds without strict complementarity assumption', Math. Program. 86(3), 615-635.
161. M. R. Hestenes and E. Stiefel (1952), 'Methods of conjugate gradients for solving linear systems', J. Res. National Bureau of Standards 49, 409-436.
162. W. Hock and K. Schittkowski (1981), Test Examples for Nonlinear Programming Codes, Vol. 187 of Lecture Notes in Economics and Mathematical Systems, Springer, Heidelberg/Berlin/New York.
163. B. Jansen, C. Roos, T. Terlaky and J.-Ph. Vial (1996), 'Primal-dual target following algorithms for linear programming', Ann. Oper. Res. 62, 197-231.
164. L. C. Kaufman (1999), 'Reduced storage, quasi-Newton trust region approaches to function optimization', SIAM J. Optim. 10(1), 56-69.
165. M. Kočvara and M. Stingl (2003), 'PENNON, a code for nonconvex nonlinear and semidefmite programming', Optim. Methods Software 18(3), 317-333.
166. M. Lalee, J. Nocedal and T. D. Plantenga (1998), 'On the implementation of an algorithm for large-scale equality constrained optimization', SIAM J. Optim. 8(3), 682-706.
167. R. D. Leone, A. Murli, P. M. Pardalos and G. Toraldo, eds (1998), High Performance Algorithms and Software in Nonlinear Optimization, Kluwer, Dordrecht, Netherlands.
168. M. Lescrenier (1991), 'Convergence of trust region algorithms for optimization with bounds when strict complementarity does not hold', SIAM J. Numer. Anal. 28(2), 476-495.
169. E. S. Levitin and B. T. Polyak (1966), 'Constrained minimization problems', USSR Comput. Math. Math. Phys. 6, 1-50.
170. A. S. Lewis and M. L. Overton (1996), Eigenvalue optimization, in Acta Numerica, Vol. 5, Cambridge University Press, pp. 149-190.
171. M. Lewis and S. G. Nash (2002), Practical aspects of multiscale optimization methods for VLSICAD, in Multiscale Optimization and VLSI/CAD (J. Cong and J. R. Shinnerl, eds), Kluwer, Dordrecht, Netherlands, pp. 265-291.
172. M. Lewis and S. G. Nash (2005), 'Model problems for the multigrid optimization of systems governed by differential equations', SIAM J. Sci. Comput., to appear.
173. S. Leyffer (2003), 'Mathematical programs with complementarity constraints', SIAG/OPT Views-and-News 14(1), 15-18.
174. C. Lin and J. J. More (1999a), 'Incomplete Cholesky factorizations with limited memory', SIAM J. Sci. Comput. 21(1), 24-45.
175. C. Lin and J. J. Moré (1999b), 'Newton's method for large bound-constrained optimization problems', SIAM J. Optim. 9(4), 1100-1127.
176. D. C. Liu and J. Nocedal (1989), 'On the limited memory BFGS method for large-scale optimization', Math. Program., Ser. B 45(3), 503-528.
177. D. G. Luenberger (1984), Linear and Nonlinear Programming, 2nd edn, Addison-Wesley, Reading, MA, USA.
178. L. Lukšan (1993), 'Inexact trust region method for large sparse nonlinear least-squares', Kybernetica 29(4), 305-324.
179. L. Lukšan (1994), 'Inexact trust region method for large sparse systems of nonlinear equations', J. Optim. Theory Appl. 81(3), 569-590.
180. L. Lukšan (1996), 'Hybrid methods for large sparse nonlinear least-squares', J. Optim. Theory Appl. 89(3), 575-595.
181. L. Lukšan and J. Vlček (1998), 'Indefinitely preconditioned inexact Newton method for large sparse equality constrained nonlinear programming problems', Numer. Linear Algebra Appl. 5(3), 219-247.
182. Z.-Q. Luo, J. S. Pang and D. Ralph (1996), Mathematical Programs with Equilibrium Constraints, Cambridge University Press, Cambridge.
183. Z.-Q. Luo, J. S. Pang and D. Ralph (1998), Piecewise sequential quadratic programming for mathematical programs with complementarity constraints, in Multilevel Optimization: Complexity and Applications (A. Migdala et al., ed.), Kluwer.
184. O. L. Mangasarian (1980), 'Locally unique solutions of quadratic programs, linear and non-linear complementarity problems', Math. Program., Ser. B 19(2), 200-212.
185. N. Maratos (1978), Exact penalty function algorithms for finite-dimensional and control optimization problems, PhD thesis, University of London.
186. M. Marazzi and J. Nocedal (2001), Feasibility control in nonlinear optimization, in Foundations of Computational Mathematics (A. DeVore, A. Iserles and E. Suli, eds), Vol. 284 of London Mathematical Society Lecture Note Series, Cambridge University Press, pp. 125-154.
187. D. Q. Mayne and E. Polak (1976), 'Feasible directions algorithms for optimisation problems with equality and inequality constraints', Math. Program. 11(1), 67-80.
188. S. Mehrotra (1992), 'On the implementation of a primal-dual interior point method', SIAM J. Optim. 2, 575-601.
189. J. L. Morales and J. Nocedal (2000), 'Automatic preconditioning by limited memory quasi-Newton updating', SIAM J. Optim. 10(4), 1079-1096.
190. J. J. More (2003), 'Terascale optimal PDE solvers', Talk at the ICIAM 2003 Conference in Sydney.
191. J. J. More and D. C. Sorensen (1983), 'Computing a trust region step', SIAM J. Sci. Statist. Comput. 4(3), 553-572.
192. J. J. More and D. J. Thuente (1994), 'Line search algorithms with guaranteed sufficient decrease', ACM Trans. Math. Software 20(3), 286-307.
193. J. J. More and G. Toraldo (1991), 'On the solution of large quadratic programming problems with bound constraints', SIAM J. Optim. 1(1), 93-113.
194. J. J. More and S. J. Wright (1993), Optimization Software Guide, Vol. 14 of Frontiers in Applied Mathematics, SIAM, Philadelphia, USA.
195. W. Murray and F. J. Prieto (1995), 'A sequential quadratic programming algorithm using an incomplete solution of the subproblem', SIAM J. Optim. 5(3), 590-640.
196. W. Murray and M. H. Wright (1992), Project Lagrangian methods based on the trajectories of penalty and barrier functions, Numerical Analysis Manuscript 92-01, AT&T Bell Laboratories.
197. B. A. Murtagh and M. A. Saunders (1982), 'A projected Lagrangian algorithm and its implementation for sparse non-linear constraints', Math. Program. Studies 16, 84-117.
198. K. G. Murty and S. N. Kabadi (1987), 'Some NP-complete problems in quadratic and nonlinear programming', Math. Program. 39(2), 117-129.
199. S. G. Nash (1984), 'Newton-type minimization via the Lanczos method', SIAM J. Numer. Anal. 21(4), 770-788.
200. S. G. Nash (2000a), 'A multigrid approach to discretized optimization problems', Optim. Methods Software 14, 99-116.
201. S. G. Nash (2000b), 'A survey of truncated-Newton methods', J. Comput. Appl. Math. 124, 45-59.
202. S. G. Nash and J. Nocedal (1991), 'A numerical study of the limited memory BFGS method and the truncated-Newton method for large-scale optimization', SIAM J. Optim. 1(3), 358-372.
203. S. G. Nash and A. Sofer (1990), 'Assessing a search direction within a truncated-Newton method', Oper. Res. Lett. 9(4), 219-221.
204. Y. Nesterov and A. Nemirovskii (1994), Interior-Point Polynomial Algorithms in Convex Programming, SIAM, Philadelphia, USA.
205. J. Nocedal (1980), 'Updating quasi-Newton matrices with limited storage', Math. Comp. 35, 773-782.
206. J. Nocedal (1992), Theory of algorithms for unconstrained optimization, in Acta Numerica, Vol. 1, Cambridge University Press, pp. 199-242.
207. J. Nocedal (1997), Large scale unconstrained optimization, in Duff and Watson (1997), pp. 311-338.
208. J. Nocedal and S. J. Wright (1999), Large Sparse Numerical Optimization, Series in Operations Research, Springer, Heidelberg/Berlin/New York.
209. E. O. Omojokun (1989), Trust region algorithms for optimization with nonlinear equality and inequality constraints, PhD thesis, University of Colorado, Boulder, Colorado, USA.
210. C. C. Paige and M. A. Saunders (1982), 'LSQR: an algorithm for sparse linear equations and sparse least squares', Trans. ACM Math. Software 8, 43-71.
211. E. Polak and G. Ribière (1969), 'Note sur la convergence de méthodes de directions conjuguées', Revue Francaise d'Informatique et de Recherche Opérationelle 16-R1, 35-43.
212. B. T. Polyak (1969), 'The conjugate gradient method in extremal problems', USSR Comput. Math. Math. Phys. 9, 94-112.
213. M. J. D. Powell (1977), 'Restart procedures for the conjugate gradient method', Math. Program. 12(2), 241-254.
214. M. J. D. Powell (1998), Direct search algorithms for optimization calculations, in Acta Numerica, Vol. 7, Cambridge University Press, pp. 287-336.
215. C. J. Price and Ph. L. Toint (2004), Exploiting problem structure in pattern-search methods for unconstrained optimization, Technical Report November, Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand.
216. R. Pytlak (1998), 'An efficient algorithm for large-scale nonlinear programming problems with simple bounds on the variables', SIAM J. Optim. 8(2), 532-560.
217. A. U. Raghunathan and L. T. Biegler (2003), Interior point methods for Mathematical Programs with Complementarity Constraints (MPCCs), Technical Report, Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA.
218. F. Rendl and H. Wolkowicz (1997), 'A semidefinite framework for trust region subproblems with applications to large scale minimization', Math. Program. 77(2), 273-299.
219. J. Renegar (2001), A Mathematical View of Interior-Point Methods in Convex Optimization, MPS/SIAM series on Optimization, SIAM, Philadelphia, PA, USA.
220. S. M. Robinson (1974), 'Perturbed Kuhn-Tucker points and rates of convergence for a class of nonlinear programming algorithms', Math. Program. 7(1), 1-16.
221. M. A. Saunders and J. A. Tomlin (1996), Solving regularized linear programs using barrier methods and KKT systems, Technical Report SOL 96-4, Department of EESOR, Stanford University, Stanford, CA, USA.
222. H. Scheel and S. Scholtes (2000), 'Mathematical programs with complementarity constraints: Stationarity, optimality, and sensitivity', Math. Oper. Res. 25, 1-22.
223. T. Schlick (1993), 'Modified Cholesky factorizations for sparse preconditioners', SIAM J. Sci. Comput. 14(2), 424-445.
224. J. A. Scott, Y. Hu and N. I. M. Gould (2004), An evaluation of sparse direct symmetric solvers: An introduction and preliminary findings, Numerical Analysis Group Internal Report 2004-1, Rutherford Appleton Laboratory, Chilton, Oxfordshire, UK.
225. S. Smith and L. Lasdon (1992), 'Solving large sparse nonlinear programs using GRG', ORSA J. Comput. 4, 1-15.
226. D. C. Sorensen (1997), 'Minimization of a large-scale quadratic function subject to a spherical constraint', SIAM J. Optim. 7(1), 141-161.
227. E. Spedicato, ed. (1994), Algorithms for Continuous Optimization: The State of the Art, Vol. 434 of NATO ASI Series C: Mathematical and Physical Sciences, Kluwer, Dordrecht, Netherlands.
228. T. Steihaug (1983), 'The conjugate gradient method and trust regions in large scale optimization', SIAM J. Numer. Anal. 20(3), 626-637.
229. A. Tits, A. Wächter, S. Bakhtiari, T. J. Urban and C. T. Lawrence (2003), 'A primal-dual interior-point method for nonlinear programming with strong global and local convergence properties', SIAM J. Optim. 14(1), 173-199.
230. M. J. Todd (2001), Semidefinite optimization, in Acta Numerica, Vol. 10, Cambridge University Press, pp. 515-560.
231. Ph. L. Toint (1981), Towards an efficient sparsity exploiting Newton method for minimization, in Sparse Matrices and Their Uses (I. S. Duff, ed.), Academic Press, London, pp. 57-88.
232. Ph. L. Toint (1987), 'On large scale nonlinear least squares calculations', SIAM J. Sci. Statist. Comput. 8(3), 416-435.
233. Ph. L. Toint (1988), 'Global convergence of a class of trust region methods for nonconvex minimization in Hubert space', IMA J. Numer. Anal. 8, 231-252.
234. Ph. L. Toint (1996), 'An assessment of non-monotone linesearch techniques for unconstrained optimization', SIAM J. Sci. Statist. Comput. 17(3), 725-739.
235. Ph. L. Toint (1997), 'A non-monotone trust-region algorithm for nonlinear optimization subject to convex constraints', Math. Program. 77(1), 69-94.
236. M. Ulbrich (2004a), 'A multidimensional filter trust-region method for mixed complementarity problems', Talk at ICCOPT 1, Troy, USA.
237. M. Ulbrich, S. Ulbrich and L. N. Vicente (2004), 'A globally convergence primal-dual interior-point filter method for nonlinear programming', Math. Program., Ser. B 100(2), 379-410.
238. S. Ulbrich (2004b), 'On the superlinear local convergence of a filter-SQP method', Math. Program., Ser. B 100(1), 217-245.
239. R. J. Vanderbei (1995), 'Symmetric quasi-definite matrices', SIAM J. Optim. 5, 100-113.
240. R. J. Vanderbei (1999), 'LOQO: An interior point code for quadratic programming', Optim. Methods Software 12, 451-484.
241. R. J. Vanderbei and D. F. Shanno (1999), 'An interior point algorithm for nonconvex nonlinear programming', Comput. Optim. Appl. 13, 231-252.
242. S. A. Vavasis (1990), 'Quadratic programming is is NP', Inform. Process. Lett. 36(2), 73-77.
243. S. A. Vavasis (1991), Convex quadratic programming, in Nonlinear Optimization: Complexity Issues, Oxford University Press, Oxford, pp. 36-75.
244. A. Wächter (2002), An interior point algorithm for large-scale nonlinear optimization with applications in process engineering, PhD thesis, Department of Chemical Engineering, Carnegie-Mellon University, Pittsburgh, PA, USA.
245. A. Wächter and L. T. Biegler (2000), 'Failure of global convergence for a class of interior point methods for nonlinear programming', Math. Program. 88(3), 565-574.
246. A. Wächter and L. T. Biegler (2003a), Line search filter methods for nonlinear programming: Local convergence, Technical Report RC23033(W0312-090), T. J. Watson Research Center, Yorktown Heights, NY, USA.
247. A. Wächter and L. T. Biegler (2003b), Line search filter methods for nonlinear programming: Motivation and global convergence, Technical Report RC23036(W0304-181), T. J. Watson Research Center, Yorktown Heights, NY, USA.
248. A. Wächter and L. T. Biegler (2004), On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming, Research report RC 23149, IBM T. J. Watson Research Center, Yorktown Heights, NY, USA.
249. M. H. Wright (1992), Interior methods for constrained optimization, in Acta Numerica, Vol. 1, Cambridge University Press, pp. 341-407.
250. S. J. Wright (1997), Primal-Dual Interior-Point Methods, SIAM, Philadelphia, USA.
251. H. Yamashita, H. Yabe and T. Tanabe (2004), 'A globally and superlinearly convergent primal-dual interior point trust region method for large scale constrained optimization', Math. Program. Online First DOI 10.1007/s10107-004- 0508-9.
252. Y. Ye (1997), Interior Point Algorithms, Theory and Analysis, Wiley-Interscience Series in Discrete Mathematics and Optimization, Wiley, New York, USA.
253. E. A. Yildirim and S. J. Wright (2002), 'Warm-start strategies in interior-point methods for linear programming', SIAM J. Optim. 12(3), 782-810.
254. Y. Yuan, ed. (1998), Advances in Nonlinear Programming, Kluwer, Dordrecht, Netherlands.
255. Y. Yuan (2000), 'On the truncated conjugate-gradient method', Math. Program., Ser. A 87(3), 561-573.
256. Y. Zhang (1994), 'On the convergence of a class of infeasible interior-point methods for the horizontal linear complementarity problem', SIAM J. Optim. 4(1), 208-227.
257. C. Zhu, R. H. Byrd, P. Lu and J. Nocedal (1997), 'Algorithm 778. L-BFGS-B: Fortran subroutines for large-scale bound constrained optimization', ACM Trans. Math. Software 23(4), 550-560.