Convergence properties of minimization algorithms for convex constraints using a structured trust region

SIAM Journal on Optimization

Volumn 6, Issue 4, 1996, Pages 1059-1086

  Conn, A R ^a   Gould, Nick ^b   Sartenaer, A ^c   Toint, Ph L ^c  

^a IBM T J WATSON RESEARCH CENTER   (United States)

^b RUTHERFORD APPLETON LABORATORY   (United Kingdom)

^c UNIVERSITY OF NAMUR   (Belgium)

Author keywords

Convex constraints; Large scale optimization; Partial separability; Structured problems; Trust region methods

Indexed keywords

EID: 0030497070     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623492236481     Document Type: Article

References (45)

1. I. BONGARTZ, A. R. CONN, N.I.M. GOULD, AND PH. L. TOINT, CUTE: Constrained and unconstrained testing environment, ACM Trans. Math. Software, 21 (1995), pp. 123-160.
2. J. V. BURKE AND J. J. MORÉ, On the identification of active constraints, SIAM J. Numer. Anal., 25 (1988), pp. 1197-1211.
3. J. V. BURKE, J. J. MORÉ, AND G. TORALDO, Convergence properties of trust region methods for linear and convex constraints, Math. Programming, Ser. A, 47 (1990), pp. 305-336.
4. R. H. BYRD, E. ESKOW, R. B. SCHNABEL, AND S. L. SMITH, Parallel Global Optimization: Numerical Methods, Dynamic Scheduling Methods, and Application to Molecular Configuration, Tech. Report CU-CS-553-91, Department of Computer Science, University of Colorado at Boulder, Boulder, CO, 1991.
5. R. H. BYRD, R. B. SCHNABEL, AND G. A. SCHULTZ, A trust region algorithm for nonlinearly constrained optimization, SIAM J. Numer. Anal., 24 (1987), pp. 1152-1170.
6. P. H. CALAMAI AND J. J. MORÉ, Projected gradient methods for linearly constrained problems, Math. Programming, 39 (1987), pp. 93-116.
7. R. G. CARTER, On the global convergence of trust region methods using inexact gradient information, SIAM J. Numer. Anal., 28 (1991), pp. 251-265.
8. M. R. CELIS, J. E. DENNIS, AND R. A. TAPIA, A trust region strategy for nonlinear equality constrained optimization, in Numerical Optimization 1984, P. T. Boggs, R. H. Byrd, and R. B. Schnabel, eds., Society for Industrial and Applied Mathematics, Philadelphia, PA, 1985, pp. 71-82.
9. A. R. CONN, N. I. M. GOULD, M. LESCRENIER, AND PH. L. TOINT, Performance of a multifrontal scheme for partially separable optimization, in Advances in Optimization and Numerical Analysis, Proceedings of the 6th Workshop on Optimization and Numerical Analysis, Oaxaca, Mexico. Vol. 275, Kluwer Academic Publishers. Dordrecht, the Netherlands, 1994, pp. 79-96.
10. A. R. CONN, N. I. M. GOUL, AND PH. L. TOINT, Global convergence of a class of trust region algorithms for optimization with simple bounds, SIAM J. Numer. Anal., 25 (1988), pp. 433-460. See also 26 (1989), pp. 764-767.
11. A. R. CONN, N. I. M. GOUL, AND PH. L. TOINT, Global convergence of a class of trust region algorithms for optimization with simple bounds, SIAM J. Numer. Anal., 25 (1988), pp. 433-460. See also 26 (1989), pp. 764-767.
12. _, Testing a class of methods for solving minimization problems with simple bounds on the variables, Math. Comput., 50 (1988), pp. 399-430.
13. _, 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., Society for Industrial and Applied Mathematics, Philadelphia, PA, 1990, pp. 42-51.
14. _, LANCELOT: A Fortran package for large-scale nonlinear optimization (Release A), in Springer Series in Computational Mathematics, No. 17, Springer-Verlag, Heidelberg, Berlin, New York, 1992.
15. A. R. CONN, NICK GOULD, A. SARTENAER, AND PH. L. TOINT, Global convergence of a class of trust region algorithms for optimization using inexact projections on convex constraints, SIAM J. Optim., 3 (1993), pp. 164-221.
16. _, Convergence Properties of Minimization Algorithm for Convex Constraints Using a Structured Trust Region (revised), Technical Report 94/5, Department of Mathematics, FUNDP, Namur, Belgium, 1994.
17. M. EL-ALEM, A global convergence theory for the Dennis-Celis-Tapia trust-region algorithm for constrained optimization, SIAM J. Numer. Anal., 28 (1991), pp. 266-290.
18. R. FLETCHER, Practical Methods of Optimization: Unconstrained Optimization, J. Wiley and Sons, New York, 1980.
19. D. M. GAY, Is exploiting partial separability useful? Talk at the 6th Mexico United States Workshop, Oaxaca, Mexico, January 1992.
20. D. GOLDFARB AND S. WANG, Partial-update Newton methods for unary, factorable, and partially separable optimization, SIAM J. Optim., 3 (1993), pp. 383-397.
21. A. GRIEWANK, The global convergence of partitioned BFGS on problems with convex decompositions and Lipschitzian gradients, Math. Programming, Ser. A, 50 (1991).
22. A. GRIEWANK AND PH. L. TOINT, On the unconstrained optimization of partially separable functions, in Nonlinear Optimization 1981, M. J. D. Powell, ed., Academic Press, London, New York, 1982, pp. 301-312.
23. A. GRIEWANK AND PH. L. TOINT, Numerical experiments with partially separable optimization problems, in Numerical Analysis: Proceedings Dundee 1983, Lecture Notes in Mathematics, Vol. 1066, Springer-Verlag, Berlin, 1984, pp. 203-220.
24. _, On the existence of convex decomposition of partially separable functions, Math. Programming, 28 (1984), pp. 25-49.
25. W. A. GRUVER AND E. SACHS, Algorithmic Methods in Optimal Control, Pitman, Boston, 1980.
26. M. D. HEBDEN, An Algorithm for Minimization Using Exact Second Derivatives, Technical Report T.P. 515, AERE Harwell Laboratory, Harwell, UK, 1973.
27. M. LESCRENIER, Partially separable optimization and parallel computing, in Parallel Optimization on Novel Computer Architectures, R. R. Meyer and S. Zenios, eds., A. C. Baltzer Scientific Publishing Co., Switzerland, 1989.
28. _, Convergence of trust region algorithms for optimization with bounds when strict complementarity does not hold, SIAM J. Numer. Anal., 28 (1991), pp. 476-495.
29. K. LEVENBERG, A method for the solution of certain problems in least squares, Quarterly J. Appl. Math., 2 (1944), pp. 164-168.
30. D. MARQUARDT, An algorithm for least-squares estimation of nonlinear parameters, SIAM J. Appl. Math., 11 (1963), pp. 431-441.
31. J. J. MORÉ, The Levenberg-Marquardt algorithm: Implementation and theory, in Proceedings Dundee 1977, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1978.
32. _, Recent developments in algorithms and software for trust region methods, in Mathematical Programming: The State of the Art. A. Bachem, M. Grötschel, and B. Korte, eds., Springer-Verlag, Berlin, 1983, pp. 258-287.
33. _, Trust regions and projected gradients, in System Modelling and Optimization, Lecture Notes in Control and Information Sciences, Vol. 113, Springer-Verlag, Berlin, 1988, pp. 1-13.
34. J. J. MORÉ AND G. TORALDO, On the solution of large scale quadratic programming problems with bound constraints, SIAM J. Optim., 1 (1991), pp. 93-113.
35. M. J. D. POWELL, A new algorithm for unconstrained optimization, in Nonlinear Programming, J. B. Rosen, O. L. Mangasarian, and K. Ritter, eds., Academic Press, New York, 1970.
36. _, On the global convergence of trust region algorithms for unconstrained optimization, Math. Programming, 29 (1984), pp. 297-303.
37. M. J. D. POWELL AND Y. YUAN, A trust region algorithm for equality constrained optimization, Math. Programming, 49 (1990), pp. 189-213.
38. T. STEIHAUG, The conjugate gradient method and trust regions in large scale optimization, SIAM J. Numer. Anal., 20 (1983), pp. 626-637.
39. PH. L. TOINT, Towards an efficient sparsity exploiting Newton method for minimization, in Sparse Matrices and Their Uses, I. S. Duff, ed., Academic Press, London, 1981, pp. 57-88,
40. _, Global convergence of the partitioned BFGS algorithm for convex partially separable optimization, Math. Programming, 36 (1986), pp. 290-307.
41. _, On large scale nonlinear least squares calculations, SIAM J. Sci. Statist. Comput., 8 (1987), pp. 416-435.
42. _, Global convergence of a class of trust region methods for nonconvex minimization in Hilbert space, IMA J. Numer. Anal., 8 (1988), pp. 231-252.
43. PH. L. TOINT AND D. TUYTTENS, On large scale nonlinear network optimization, Math. Programming, Ser. B. 48 (1990), pp. 125-159.
44. _, LSNNO: A Fortran subroutine for solving large scale nonlinear network optimization problems, ACM Trans. Math. Software, 18 (1992), pp. 308-328.
45. A. VARDI, A trust region algorithm for equality constrained minimization: Convergence properties and implementation, SIAM J. Numer. Anal., 22 (1985), pp. 575-591.