An augmented Lagrangian method for a class of inverse quadratic programming problems

Applied Mathematics and Optimization

Volumn 61, Issue 1, 2010, Pages 57-83

  Zhang, Jianzhong ^a   Zhang, Liwei ^b  

^a BNU HKBU UNITED INTERNATIONAL COLLEGE   (China)

^b DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Inverse optimization; Newton method; Quadratic programming; Rate of convergence; The augmented Lagrangian method; The cone of positive semidefinite matrices

Indexed keywords

AUGMENTED LAGRANGIAN METHODS; INVERSE OPTIMIZATION; NEWTON METHOD; NEWTON METHODS; POSITIVE SEMIDEFINITE MATRICES; RATE OF CONVERGENCE; THE AUGMENTED LAGRANGIAN METHOD;

APPROXIMATION THEORY; INVERSE PROBLEMS; NEWTON-RAPHSON METHOD; NUMERICAL ANALYSIS; OPTIMIZATION; QUADRATIC PROGRAMMING; SINGULAR VALUE DECOMPOSITION;

LAGRANGE MULTIPLIERS;

EID: 73349086204     PISSN: 00954616     EISSN: 14320606     Source Type: Journal    
DOI: 10.1007/s00245-009-9075-z     Document Type: Article

References (32)

1. R.K. Ahuja J.B. Orlin 2001 Inverse optimization Oper. Res. 49 771 183 1163.90764 10.1287/opre.49.5.771.10607 1860425
2. R.K. Ahuja J.B. Orlin 2002 Combinatorial algorithms for inverse network flow problems Networks 40 181 187 1026.90089 10.1002/net.10048 1938783 (Pubitemid 37218329)
3. Bertsekas, D.P.: Constrained Optimization and Lagrange Multiplier Methods. Academic Press, New York (1982)
4. R.E. Burkard Y. Lin J. Zhang 2004 Weight reduction problems with certain bottleneck objectives Eur. J. Oper. Res. 153 191 199 1137.90689 10.1016/S0377-2217(02)00713-0 2037212
5. W.R. Burton Ph.L. Toint 1992 On an instance of the inverse shortest paths problem Math. Program. 53 45 61 0756.90089 10.1007/BF01585693 1151764
6. M.C. Cai X.G. Yang J. Zhang 1999 The complexity analysis of the inverse center location problem J. Global Optim. 15 213 218 0978.90065 10.1023/A:1008360312607 1714066
7. S. Carr W. Lovejoy 2000 The inverse newsvendor problem: choosing an optimal demand portfolio for capacitated resources Manag. Sci. 46 912 927 10.1287/mnsc.46.7.912.12036
8. Clarke, F.H.: Optimization and Nonsmooth Analysis. Wiley, New York (1983)
9. R. Dembo D. Rosen 1999 The practice of portfolio replication: a practical overview of forward and inverse problems Ann. Oper. Res. 85 267 284 0920.90006 10.1023/A:1018977929028 1685635
10. 1 functions and the Maratos effect Oper. Res. Lett. 17 131 137 0843.90108 10.1016/0167-6377(94) 00059-F 1342260
11. Facchinei, F., Pang, J.-S.: Finite-Dimensional Variational Inequalities and Complementarity Problems, vol. I. Springer, New York (2003)
12. Facchinei, F., Pang, J.-S.: Finite-Dimensional Variational Inequalities and Complementarity Problems, vol. II. Springer, New York (2003)
13. Golshtein, E.G., Tretyakov, N.V.: Modified Lagrangians and Monotone Maps in Optimization. Wiley, New York (1989)
14. Hartley, M.J., Bakshi, G.S.: Markowitz models of portfolio selection: the inverse problem. (October 1998)
15. C. Heuberger 2004 Inverse combinatorial optimization: a survey on problems, methods and results J. Comb. Optim. 8 329 361 1084.90035 10.1023/B:JOCO.0000038914.26975.9b 2092264
16. Hiriart-Urruty, J.-B., Lemaréchal, C.: Convex Analysis and Minimization Algorithms. Springer, Berlin (1993)
17. 1,1 data Appl. Math. Optim. 11 43 56 0542.49011 10.1007/BF01442169 726975
18. G. Iyengar W. Kang 2005 Inverse conic programming and applications Oper. Res. Lett. 33 319 330 1140.90465 10.1016/j.orl.2004.04.007 2108284
19. J. Malick 2004 A dual approach to semidefinite least-squares problems SIAM J. Matrix Anal. Appl. 26 1 272 284 1080.65027 10.1137/S0895479802413856 2112861
20. R. Mifflin 1977 Semismooth and semiconvex functions in constrained optimization SIAM J. Control Optim. 15 957 972 461556
21. L. Qi J. Sun 1993 A nonsmooth version of Newton's method Math. Program. 58 353 367 10.1007/BF01581275 1216791
22. R.T. Rockafellar 1973 A dual approach to solving nonlinear programming problems by unconstrained optimization Math. Program. 5 354 373 0279.90035 10.1007/BF01580138 371416
23. R.T. Rockafellar 1973 The multiplier method of Hestenes and Powell applied to convex programming J. Optim. Theory Appl. 12 555 562 0254.90045 10.1007/BF00934777 334953
24. Rockafellar, R.T.: Conjugate Duality and Optimization. SIAM, Philadelphia (1974)
25. Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Springer, New York (1998)
26. A. Shapiro 1990 On concepts of directional differentiability J. Optim. Theory Appl. 66 477 487 0682.49015 10.1007/BF00940933 1080259
27. D. Sun J. Sun 2002 Semismooth matrix valued functions Math. Oper. Res. 27 150 169 1082.49501 10.1287/moor.27.1.150.342 1886224
28. D. Sun J. Sun L. Zhang 2008 The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming Math. Program. 114 349 391 05284681 10.1007/s10107-007-0105-9 2393047
29. J. Zhang Z. Liu 1996 Calculating some inverse linear programming problems J. Comput. Appl. Math. 72 261 273 0856.65069 10.1016/0377-0427(95)00277-4 1406213 (Pubitemid 126380098)
30. J. Zhang Z. Liu 1999 A further study on inverse linear programming problems J. Comput. Appl. Math. 106 345 359 0971.90051 10.1016/S0377-0427(99) 00080-1 1696416
31. J. Zhang Z. Ma 1999 Solution structure of some inverse combinatorial optimization problems J. Comb. Optim. 3 127 139 0932.90034 10.1023/A: 1009829525096 1702520
32. Zhao, X., Sun, D.F., Toh, K.-C.: A Newton-CG augmented Lagrangian method for semidefinite programming. Optimization (Online) (2008)