Stable zero duality gaps in convex programming: Complete dual characterisations with applications to semidefinite programs

Journal of Mathematical Analysis and Applications

Volumn 360, Issue 1, 2009, Pages 156-167

  Jeyakumar, V ^a   Li, G Y ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Convex optimisation; Dual conditions; Second order cone programming; Semidefinite programming; Stable zero duality gaps

Indexed keywords

EID: 68049121845     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2009.06.043     Document Type: Article

References (23)

1. Auslender A., and Teboulle M. Asymptotic Cones and Functions in Optimisation and Variational Inequalities. Springer Monogr. Math. (2003), Springer-Verlag, New York
2. Auslender A. Existence of optimal solutions and duality results under weak conditions. Math. Program. Ser. A 88 (2000) 45-59
3. Bonnans J.F., and Shapiro A. Perturbation Analysis of Optimization Problems (2000), Springer, New York
4. Ban L., and Song W. Duality gap of the conic convex constrained optimisation problems in normed spaces. Math. Program. Ser. A 119 (2009) 195-214
5. Burachik R.S., and Jeyakumar V. A new geometric condition for Fenchel's duality in infinite dimensional spaces. Math. Program. Ser. B 104 2-3 (2005) 229-233
6. Burachik R.S., Jeyakumar V., and Wu Z.Y. Necessary and sufficient conditions for stable conjugate duality. J. Nonlinear Anal. Ser. A 64 (2006) 1998-2006
7. Canovas M.J., Klatte D., Lopez M.A., and Parra J. Metric regularity in convex semi-infinite optimisation under canonical perturbations. SIAM J. Optim. 18 (2007) 717-732
8. Goberna M.A., Gomez S., Guerra F., and Todorov M.I. Sensitivity analysis in linear semi-infinite programming: Perturbing cost and right-hand-side coefficients. European J. Oper. Res. 181 (2007) 1069-1085
9. Jeyakumar V. A note on strong duality in convex semidefinite optimization: Necessary and sufficient conditions. Optim. Lett. 2 (2008) 15-25
10. Jeyakumar V. Constraint qualifications characterizing Lagrangian duality in convex optimization. J. Optim. Theory Appl. 136 (2008) 31-41
11. Jeyakumar V., and Lee G.M. Complete characterizations of stable Farkas' lemma and cone-convex programming duality. Math. Program. Ser. A 114 (2008) 335-347
12. Jeyakumar V., and Wolkowicz H. Zero duality gaps in infinite dimensional programming. J. Optim. Theory Appl. 67 (1990) 87-108
13. Jeyakumar V., and Li G. New dual constraint qualifications characterizing zero duality gaps of convex programs and semidefinite programs. Nonlinear Anal. (2009) 10.1016/j.na.2009.05.009 in press
14. G. Li, V. Jeyakumar, No duality gaps for convex programs with separable inequality constraints, School of Mathematics Preprint, 2008, Math. Oper. Res., submitted for publication
15. Li C., Ng K.F., and Pong T.K. The SECQ, linear regularity and the strong CHIP for infinite system of closed convex sets in normed linear spaces. SIAM J. Optim. 18 (2007) 643-665
16. Pataki G. On the closedness of the linear image of a closed convex cone. Math. Oper. Res. 32 2 (2008) 395-412
17. Ramana M.V., Tunçel L., and Wolkowicz H. Strong duality for semidefinite programming. SIAM J. Optim. 7 (1997) 644-662
18. Rockafellar T. Conjugate Duality and Optimization (1974), Society for Industrial and Applied Mathematics, Philadelphia
19. Schurr S.P., Tits A.L., and O'Leary P. Universal duality in conic convex optimization. Math. Program. Ser. A 109 (2007) 69-88
20. Tseng P. Some convex programs without a duality gap. Math. Program. Ser. B 116 (2009) 553-573
21. Shapiro A. On duality theory of convex semi-infinite programming. Optimization 54 (2005) 535-543
22. Wolkowicz H., Saigal R., and Vandenberghe L. Handbook of Semidefinite Programming. Internat. Ser. Oper. Res. Management Sci. vol. 27 (2000), Kluwer, Dordrecht
23. Zalinescu C. Convex Analysis in General Vector Spaces (2002), World Scientific