A weaker regularity condition for subdifferential calculus and Fenchel duality in infinite dimensional spaces

Nonlinear Analysis, Theory, Methods and Applications

Volumn 64, Issue 12, 2006, Pages 2787-2804

  Boţ, Radu Ioan ^a   Wanka, Gert ^a  

^a CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Fenchel duality; Regularity condition; Strong conical hull intersection property; Subdifferential sum formula

Indexed keywords

DIFFERENTIATION (CALCULUS); FUNCTIONS; OPTIMIZATION; PROBLEM SOLVING; SET THEORY;

FENCHEL DUALITY; REGULARITY CONDITIONS; STRONG CONICAL HULL INTERSECTION PROPERTY; SUBDIFFERENTIAL SUM FORMULA;

NUMERICAL ANALYSIS;

EID: 33645961296     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2005.09.017     Document Type: Article

References (25)

1. Attouch H., and Brézis H. Duality for the sum of convex functions in general Banach spaces. In: Barroso J.A. (Ed). Aspects of Mathematics and its Applications (1986), North Holland, Amsterdam 125-133
2. Bauschke H.H. Proof of a conjecture by Deutsch, Li, and Swetits on duality of optimization problems. J. Optim. Theory Appl. 102 (1999) 697-703
3. Bauschke H.H., Borwein J.M., and Li W. Strong conical hull intersection property, bounded linear regularity, Jameson's property ( G ), and error bounds in convex optimization. Math. Programming 86 (1999) 135-160
4. Borwein J.M., and Lewis A.S. Partially finite convex programming. I. Quasi relative interiors and duality theory. Math. Programming 57 (1992) 15-48
5. Boţ R.I., Kassay G., and Wanka G. Strong duality for generalized convex optimization problems. J. Optim. Theory Appl. 127 1 (2005) 45-70
6. R.I. Boţ, G. Wanka, An alternative formulation for a new closed cone constraint qualification, Nonlinear Anal.: Theory, Methods Appl., to appear.
7. Boţ R.I., and Wanka G. Farkas-type results with conjugate functions. SIAM J. Optim. 15 2 (2005) 540-554
8. Burachik R.S., and Jeyakumar V. A dual condition for the convex subdifferential sum formula with applications. J. Convex Anal. 12 2 (2005) 279-290
9. Burachik R.S., and Jeyakumar V. A simpler closure condition for the normal cone intersection formula. Proc. Amer. Math. Soc. 133 6 (2005) 1741-1748
10. Deutsch F., Li W., and Swetits J. Fenchel duality and the strong conical hull intersection property. J. Optim. Theory Appl. 102 (1999) 681-695
11. Deutsch F., Li W., and Ward J.D. A dual approach to constrained interpolation from a convex subset of Hilbert space. J. Approximation Theory 90 (1997) 385-414
12. Deutsch F., Li W., and Ward J.D. Best approximation from the intersection of a closed convex set and a polyhedron in Hilbert space, weak Slater conditions, and the strong conical hull intersection property. SIAM J. Optim. 10 (1999) 252-268
13. Ekeland I., and Temam R. Convex Analysis and Variational Problems (1976), North-Holland Publishing Company, Amsterdam
14. Fitzpatrick S.P., and Simons S. The conjugates, compositions and marginals of convex functions. J. Convex Anal. 8 (2001) 423-446
15. Gowda M.S., and Teboulle M. A comparison of constraint qualifications in infinite-dimensional convex programming. SIAM J. Control Optim. 28 (1990) 925-935
16. Holmes R.B. Geometric Functional Analysis (1975), Springer, Berlin
17. Jeyakumar V., and Wolkowicz H. Generalizations of Slater's constraint qualification for infinite convex programs. Math. Programming 57 (1992) 85-102
18. Ng K.F., and Song W. Fenchel duality in infinite-dimensional setting and its applications. Nonlinear Anal. 25 (2003) 845-858
19. Rockafellar R.T. Extension of Fenchel's duality theorem for convex functions. Duke Math. J. 33 (1966) 81-89
20. Rockafellar R.T. Conjugate duality and optimization, Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics 16 (1974), Society for Industrial and Applied Mathematics, Philadelphia
21. Rodrigues B. The Fenchel duality theorem in Fréchet spaces. Optimization 21 (1990) 13-22
22. Rodrigues B., and Simons S. Conjugate functions and subdifferentials in nonnormed situations for operators with complete graphs. Nonlinear Anal. 12 (1988) 1069-1078
23. Strömberg T. The operation of infimal convolution. Diss. Math. 352 (1996)
24. Zãlinescu C. A comparison of constraint qualifications in infinite-dimensional convex programming revisited. J. Aust. Math. Soc., Ser. B 40 (1999) 353-378
25. Zãlinescu C. Convex Analysis in General Vector Spaces (2002), World Scientific, Singapore