Ir al contenido

Documat


Infimal convolution, c-subdifferentiability, and Fenchel duality in evenly convex optimization

    1. [1] Universitat d'Alacant

      Universitat d'Alacant

      Alicante, España

  • Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 20, Nº. 2, 2012, págs. 375-396
  • Idioma: inglés
  • DOI: 10.1007/s11750-011-0208-6
  • Enlaces
  • Resumen
    • In this paper we deal with strong Fenchel duality for infinite-dimensional optimization problems where both feasible set and objective function are evenly convex. To this aim, via perturbation approach, a conjugation scheme for evenly convex functions, based on generalized convex conjugation, is used. The key is to extend some well-known results from convex analysis, involving the sum of the epigraphs of two conjugate functions, the infimal convolution and the sum formula of ε-subdifferentials for lower semicontinuous convex functions, to this more general framework.

  • Referencias bibliográficas
    • Fenchel W (1952) A remark on convex sets and polarity. Comm Sèm Math Univ Lund, Suppl 82–89 (Medd Lunds Algebra Univ Math Sem).
    • ATTOUCH, H. and BREZIS, H., 1986. Duality of the sum of convex functions in general Banach spaces. In: J.A. BARROSO, ed, Aspects of mathematics...
    • BOŢ, R.I., 2010. Conjugate duality in convex optimization. Berlin: Springer.
    • BOŢ, R.I., GRAD, S.M. and WANKA, G., 2009a. Duality in vector optimization. Berlin: Springer.
    • BOŢ, R.I., GRAD, S.M. and WANKA, G., 2009b. Generalized Moreau–Rockafellar results for composed convex functions. Optimization, 58.
    • BOŢ, R.I. and WANKA, G., 2006. A weaker regularity condition for subdifferential calculus and Fenchel duality in infinite dimensional spaces....
    • BURACHIK, R.S. and JEYAKUMAR, V., 2005a. A dual condition for the convex subdifferential sum formula with applications. J Convex Anal, 12.
    • BURACHIK, R.S. and JEYAKUMAR, V., 2005b. A new geometric condition for Fenchel’s duality in infinite dimensional spaces. Math Program, Ser...
    • DANIILIDIS, A. and MARTÍNEZ-LEGAZ, J.E., 2002. Characterizations of evenly convex sets and evenly quasiconvex functions. J Math Anal Appl,...
    • EKELAND, I. and TEMAM, R., 1976. Convex analysis and variational problems. Amsterdam: North-Holland.
    • GOBERNA, M.A., JEYAKUMAR, V. and LÓPEZ, M.A., 2008. Necessary and sufficient constraint qualifications for solvability of systems of infinite...
    • GOBERNA, M.A., JORNET, V. and RODRÍGUEZ, M.M.L., 2003. On linear systems containing strict inequalities. Linear Algebra Appl, 360.
    • GOBERNA, M.A. and RODRÍGUEZ, M.M.L., 2006. Analyzing linear systems containing strict inequalities via evenly convex hulls. Eur J Oper Res,...
    • GOWDA, M.S. and TEBOULLE, M., 1990. A comparison of constraint qualifications in infinite-dimensional convex programming. SIAM J Control Optim,...
    • KLEE, V., MALUTA, E. and ZANCO, C., 2007. Basic properties of evenly convex sets. J Convex Anal, 14.
    • LI, C., FANG, D., LÓPEZ, G. and LÓPEZ, M.A., 2009. Stable and total Fenchel duality for convex optimization problems in locally convex spaces....
    • MARTÍNEZ-LEGAZ, J.E., 2005. Generalized convex duality and its economic applications. In: N. HADJISAVVAS, S. KOMLÓSI and S. SCHAIBLE, eds,...
    • MARTÍNEZ-LEGAZ, J.E., 1988. Quasiconvex duality theory by generalized conjugation methods. Optimization, 19.
    • MARTÍNEZ-LEGAZ, J.E., 1983. A generalized concept of conjugation. In: J.-.B. HIRIART-URRUTY, W. OETTLI and J. STOER, eds, Optimization: theory...
    • MARTÍNEZ-LEGAZ, J.E. and VICENTE-PÉREZ, J., 2011. The e-support function of an e-convex set and conjugacy for e-convex functions. J Math Anal...
    • MOREAU, J.J., 1970. Inf-convolution, sous-additivité, convexité des fonctions numériques. J Math Pures Appl, 49.
    • NG, K.F. and SONG, W., 2003. Fenchel duality in infinite-dimensional setting and its applications. Nonlinear Anal, 55.
    • PASSY, U. and PRISMAN, E.Z., 1984. Conjugacy in quasiconvex programming. Math Program, 30.
    • PHELPS, R.R., 1993. Convex functions, monotone operators and differentiability. New York: Springer.
    • ROCKAFELLAR, R.T., 1974. Conjugate duality and optimization. Philadelphia: SIAM.
    • ROCKAFELLAR, R.T., 1970. Convex analysis. Princeton: Princeton University Press.
    • ROCKAFELLAR, R.T., 1966. Extension of Fenchel’s duality theorem for convex functions. Duke Math J, 33.
    • RODRÍGUEZ, M.M.L. and VICENTE-PÉREZ, J., 2011. On evenly convex functions. J Convex Anal, 18.
    • ZĂLINESCU, C., 2002. Convex analysis in general vector spaces. Singapore: World Scientific.

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno