An alternative formulation for a new closed cone constraint qualification

Nonlinear Analysis, Theory, Methods and Applications

Volumn 64, Issue 6, 2006, Pages 1367-1381

  Boţ, Radu Ioan ^a   Wanka, Gert ^a  

^a CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Conjugate duality; Constraint qualifications; Convex optimization; Weak and strong duality

Indexed keywords

OPTIMIZATION; PROBLEM SOLVING; THEOREM PROVING;

CONJUGATE DUALITY; CONSTRAINT QUALIFICATIONS; CONVEX OPTIMIZATION; WEAK AND STRONG DUALITY;

CONSTRAINT THEORY;

EID: 30944465215     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2005.06.041     Document Type: Article

References (19)

1. J.M. Borwein A Lagrange multiplier theorem and a sandwich theorem for convex relations Math. Scand. 48 1981 189 204
2. R.I. Boţ, S.M. Grad, and G. Wanka Fenchel-Lagrange versus geometric duality in convex optimization J. Optim. Theory Appl. 129 1 2006
3. R.I. Boţ, G. Kassay, and G. Wanka Strong duality for generalized convex optimization problems J. Optim. Theory Appl. 127 1 2005
4. R.I. Boţ, and G. Wanka Farkas-type results with conjugate functions SIAM J. Optim. 15 2 2005 540 554
5. R.S. Burachik, and V. Jeyakumar A dual condition for the convex subdifferential sum formula with applications J. Convex Anal. 12 2 2005
6. R.S. Burachik, and V. Jeyakumar A simpler closure condition for the normal cone intersection formula Proc. Am. Math. Soc. 133 6 2005 1741 1748
7. I. Ekeland, and R. Temam Convex Analysis and Variational Problems 1976 North-Holland Publishing Company Amsterdam
8. M.S. Gowda, and M. Teboulle A comparison of constraint qualifications in infinite-dimensional convex programming SIAM J. Control Optim. 28 4 1990 925 935
9. R.B. Holmes Geometric Functional Analysis 1975 Springer Berlin
10. V. Jeyakumar Characterizing set containments involving infinite convex constraints and reverse-convex constraints SIAM J. Optim. 13 4 2003 947 959
11. V. Jeyakumar, N. Dinh, G.M. Lee, A new closed cone constraint qualification for convex optimization, Applied Mathematical Report AMR04/8, University of New South Wales, Sydney, Australia, 2004.
12. V. Jeyakumar, G.M. Lee, and N. Dinh New sequential Lagrange multiplier conditions characterizing optimality without constraint qualification for convex programs SIAM J. Optim. 14 2 2003 534 547
13. V. Jeyakumar, A.M. Rubinov, B.M. Glover, and Y. Ishizuka Inequality systems and global optimization J. Math. Anal. and Appl. 202 1996 900 919
14. V. Jeyakumar, and H. Wolkowicz Generalizations of Slater's constraint qualification for infinite convex programs Math. Programm. 57 1 1992 85 102
15. V. Jeyakumar, and A. Zaffaroni Asymptotic conditions for weak and proper optimality in infinite dimensional convex vector optimization Numer. Funct. Anal. Optim. 17 3&4 1996 323 343
16. R.T. Rockafellar, Conjugate duality and optimization, Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, vol. 16, Society for Industrial and Applied Mathematics, Philadelphia, 1974.
17. G. Wanka, R.I. Boţ, On the relations between different dual problems in convex mathematical programming, in: P. Chamoni, R. Leisten, A. Martin, J. Minnemann, H. Stadtler (Eds.), Operations Research Proceedings 2001, Springer, Berlin, 2002, pp. 255-262.
18. C. Zãlinescu A comparison of constraint qualifications in infinite-dimensional convex programming revisited J. Aus. Math. Soc. Ser. B 40 3 1999 353 378
19. C. Zãlinescu Convex Analysis in General Vector Spaces 2002 World Scientific Singapore