Second-order negative-curvature methods for box-constrained and general constrained optimization

Computational Optimization and Applications

Volumn 45, Issue 2, 2010, Pages 209-236

  Andreani, R ^a   Birgin, E G ^b   Martinez J M ^a   Schuverdt, M L ^a  

^a UNIVERSITY OF CAMPINAS   (Brazil)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Augmented Lagrangians; Constraint qualifications; Global convergence; Nonlinear programming; Optimality conditions; Second order conditions

Indexed keywords

CURVE FITTING; LAGRANGE MULTIPLIERS; NONLINEAR PROGRAMMING; NUMERICAL METHODS;

AUGMENTED LAGRANGIANS; CONSTRAINT QUALIFICATION; GLOBAL CONVER-GENCE; OPTIMALITY CONDITIONS; SECOND-ORDER CONDITIONS;

CONSTRAINED OPTIMIZATION;

EID: 77950517780     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-009-9240-y     Document Type: Conference Paper

References (38)

1. R. Andreani J.M. Martínez M.L. Schuverdt 2005 On the relation between the Constant Positive Linear Dependence condition and quasinormality constraint qualification J. Optim. Theory Appl. 125 473 485 1125.90058 10.1007/s10957-004-1861-9 2136506 (Pubitemid 40572581)
2. R. Andreani E.G. Birgin J.M. Martínez M.L. Schuverdt 2007 On Augmented Lagrangian Methods with general lower-level constraints SIAM J. Optim. 18 1286 1309 1151.49027 10.1137/060654797 2373302
3. R. Andreani J.M. Martínez M.L. Schuverdt 2007 On second-order optimality conditions for nonlinear programming Optimization 56 529 542 1172.90490 10.1080/02331930701618617 2362704
4. M. Andretta E.G. Birgin J.M. Martínez 2005 Practical active-set Euclidean trust-region method with spectral projected gradients for bound-constrained minimization Optimization 54 305 325 1079.65070 10.1080/02331930500100270 2148086 (Pubitemid 40856204)
5. Anitescu, M.: Degenerate nonlinear programming with a quadratic growth condition. SIAM J. Optim. 1116-1135 (2000)
6. E.G. Birgin J.M. Martínez 2001 A box constrained optimization algorithm with negative curvature directions and spectral projected gradients Computing (Suppl.) 15 49 60
7. E.G. Birgin J.M. Martínez 2002 Large-scale active-set box-constrained optimization method with spectral projected gradients Comput. Optim. Appl. 23 101 125 1031.90012 10.1023/A:1019928808826 1931362 (Pubitemid 35167001)
8. E.G. Birgin J.M. Martínez 2008 Structured minimal-memory inexact quasi-Newton method and secant preconditioners for Augmented Lagrangian optimization Comput. Optim. Appl. 39 1 16 1147.90412 10.1007/s10589-007-9050-z 2365913
9. E.G. Birgin J.M. Martínez M. Raydan 2000 Nonmonotone spectral projected gradient methods on convex sets SIAM J. Optim. 10 1196 1211 1047.90077 10.1137/S1052623497330963 1777088
10. E.G. Birgin J.M. Martínez M. Raydan 2001 Algorithm 813: SPG-Software for convex-constrained optimization ACM Trans. Math. Softw. 27 340 349 1070.65547 10.1145/502800.502803 (Pubitemid 33654982)
11. E.G. Birgin J.M. Martínez M. Raydan 2003 Inexact Spectral Projected Gradient methods on convex sets IMA J. Numer. Anal. 23 539 559 1047.65042 10.1093/imanum/23.4.539 2011339
12. R.H. Byrd R.B. Schnabel G.A. Shultz 1987 A trust region algorithm for nonlinearly constrained optimization SIAM J. Numer. Anal. 24 1152 1170 0631.65068 10.1137/0724076 909071
13. T.F. Coleman J. Liu W. Yuan 2002 A new trust-region algorithm for equality constrained optimization Comput. Optim. Appl. 21 177 199 0988.90034 10.1023/A:1013764800871 1883753 (Pubitemid 34168105)
14. A.R. Conn N.I.M. Gould D. Orban Ph.L. Toint 2000 A primal-dual trust region algorithm for non-convex nonlinear programming Math. Program. 87 215 249 0970.90116 10.1007/s101070050112 1763849
15. Conn, A.R., Gould, N.I.M., Toint, Ph.L.: Trust Region Methods. MPS/SIAM Series on Optimization. SIAM, Philadelphia (2000)
16. J.E. Dennis L.N. Vicente 1997 On the convergence theory of trust-region-based algorithms for equality-constrained optimization SIAM J. Optim. 7 527 550 10.1137/S1052623494278347 1479607
17. J.E. Dennis M. Heinkenschloss L.N. Vicente 1998 Trust-region interior-point SQP algorithms for a class of nonlinear programming problems SIAM J. Control Optim. 36 1750 1794 0921.90137 10.1137/S036012995279031 1632552
18. G. Di Pillo S. Lucidi L. Palagi 2005 Convergence to second-order stationary points of a primal-dual algorithm model for nonlinear programming Math. Oper. Res. 30 897 915 05279648 10.1287/moor.1050.0150 2185821 (Pubitemid 43134182)
19. F. Facchinei S. Lucidi 1998 Convergence to second order stationary points in inequality constrained optimization Math. Oper. Res. 23 746 766 0977.90049 10.1287/moor.23.3.746 1653742
20. Fletcher, R.: Practical Methods of Optimization. Wiley, New York (1987)
21. A. Forsgren W. Murray 1997 Newton methods for large-scale linear inequality constrained problems SIAM J. Optim. 7 132 176 10.1137/ S1052623494279122 1430562
22. N.I.M. Gould S. Lucidi M. Roma Ph.L. Toint 2000 Exploiting negative curvature directions in linesearch methods for unconstrained optimization Optim. Methods Softw. 14 75 98 0988.90039 10.1080/10556780008805794 1809604
23. N.I.M. Gould D. Orban Ph.L. Toint 2003 CUTEr and SifDec: A constrained and unconstrained testing environment ACM Trans. Math. Softw. 29 373 394 1068.90526 10.1145/962437.962439 2077337 (revisited)
24. W.W. Hager H.C. Zhang 2006 A new active set algorithm for box constrained optimization SIAM J. Optim. 17 526 557 1165.90570 10.1137/050635225 2247750 (Pubitemid 46798079)
25. M.R. Hestenes 1969 Multiplier and gradient methods J. Optim. Theory Appl. 4 303 320 0174.20705 10.1007/BF00927673 271809
26. E.S. Levitin A.A. Milyutin N.P. Osmolovskii 1978 Higher order conditions for a local minimum in problems with constraints Russian Math. Surv. 33 97 168 0456.49015 10.1070/RM1978v033n06ABEH003885 526013
27. O.L. Mangasarian S. Fromovitz 1967 The Fritz-John necessary optimality conditions in presence of equality and inequality constraints J. Math. Anal. Appl. 17 37 47 0149.16701 10.1016/0022-247X(67)90163-1 207448
28. G.P. Mccormick 1977 A modification of Armijo's step-size rule for negative curvature Math. Program. 13 111 115 0367.90100 10.1007/BF01584328 461907
29. J.J. Moré D.C. Sorensen 1979 On the use of directions of negative curvature in a modified Newton method Math. Program. 16 1 20 0394.90093 10.1007/BF01582091
30. Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, New York (1999)
31. Powell, M.J.D.: A method for nonlinear constraints in minimization problems. In: Fletcher, R. (ed.) Optimization, pp. 283-298. Academic Press, New York (1969)
32. L. Qi Z. Wei 2000 On the constant positive linear dependence condition and its application to SQP methods SIAM J. Optim. 10 963 981 0999.90037 10.1137/S1052623497326629 1777075
33. R.T. Rockafellar 1974 Augmented Lagrange multiplier functions and duality in nonconvex programming SIAM J. Control Optim. 12 268 285 0257.90046 10.1137/0312021 384163
34. R.T. Rockafellar 1993 Lagrange multipliers and optimality SIAM Rev. 35 183 238 0779.49024 10.1137/1035044 1220880
35. G.A. Shultz R.B. Schnabel R.H. Byrd 1985 A family of trust-region-based algorithms for unconstrained minimization with strong global convergence properties SIAM J. Numer. Anal. 22 47 67 0574.65061 10.1137/0722003 772882
36. D.C. Sorensen 1982 Newton's method with a model trust region modification SIAM J. Numer. Anal. 19 409 426 0483.65039 10.1137/0719026 650060
37. A. Wächter L.T. Biegler 2006 On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming Math. Program. 106 25 57 1134.90542 10.1007/s10107-004-0559-y 2195616 (Pubitemid 41813168)
38. J. Zhang C. Xu 1999 A class of indefinite dogleg path methods for unconstrained minimization SIAM J. Optim. 9 646 667 0953.90053 10.1137/S105262349627523X 1681051