Duality gap of the conic convex constrained optimization problems in normed spaces

Mathematical Programming

Volumn 119, Issue 2, 2009, Pages 195-214

  Ban, Liqun ^a   Song, Wen ^b  

^a HARBIN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b HARBIN NORMAL UNIVERSITY   (China)

Author keywords

Conical convex constrained optimization; D(y) property; Normed spaces; S convex mapping; Zero duality gap

Indexed keywords

CONVEX OPTIMIZATION;

CONICAL-CONVEX CONSTRAINED OPTIMIZATION; D(Y) PROPERTY; NORMED SPACES; S-CONVEX MAPPING; ZERO DUALITY GAP;

CONSTRAINED OPTIMIZATION;

EID: 62249126332     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-008-0207-z     Document Type: Article

References (19)

1. A. Auslender 2000 Existence of optimal solutions and duality results under weak conditions Math. Program. Ser. A 88 45 59
2. Bonnans, J.F., Shapiro, A.: Perturbation Analysis of Optimization Problems. Springer, New York (2000)
3. R.I. Boţ G. Wanka 2006 An alternative formulation for a new closed cone constraint qualification Nonlinear Anal. 64 1367 1381
4. Boţ, R.I., Grad, S.-M., Wanka, G.: On strong and total Lagrange duality for convex optimization problems. J. Math. Anal. Appl. (to appear) doi: 10.1016/j.jmaa. 2007.04.071
5. Borwein, J.M., Lewis, A.S.: Convex Analysis and Nonlinear Optimization: Theory and Examples. Springer, New York (2000)
6. T. Champion 2004 Duality gap in convex programming Math. Program. 99 487 498
7. F. Ferro 1989 A minimax theorem for vector-valued functions J. Optim. Theory Appl. 60 19 31
8. F. Ferro 1997 Optimization and stability results through cone lower semicontinuity Set-Valued Anal. 7 365 375
9. V. Jeyakumar H. Wolkowicz 1990 Zero duality gaps in infinite-dimensional programming J. Optim. Theory Appl. 67 87 108
10. V. Jeyakumar 2006 The strong conical hull intersection property for convex programming Math. Program. 106 81 92
11. Jeyakumar, V., Song, W., Dinh, N., Lee, G.M.: Stable strong duality in convex optimization, Applied Mathematics Report AMR 05/22, University of New South Wales, Sydney (2005)
12. Klerk, E. de Roos, C., Terlaky, T.: Nonlinear Optimization. University of Waterloo (2004)
13. B. Kummer 1981 Stability and weak duality in convex programming without regularity Wiss. Z. Humboldt-Univ. Berlin Math. Natur. Reihe 30 381 386
14. S. Li 2000 A constraint qualification for convex programming Acta Math. Appl. Sinica (English Ser.) 16 362 365
15. Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)
16. Rockafellar, R.T.: Conjugate duality and optimization. Society for Industrial and Applied Mathematics (1989), First published in 1974
17. Tseng, P.: Some convex programs without a duality gap. Math. Program. Ser. B. (to appear) doi: 10.1007/s10107-007-0110-z
18. L. Vandenberghe S. Boyd 1996 Semidefinite programming SIAM Rev. 38 49 95
19. Zǎlinescu, C.: Convex Analysis in General Vector Spaces. World Scientific, Singapore (2002)