2014· Journal of Convex Analysis· Vol 21, pp. 1007-1022· 0 citations· 9 references
Abstract
Convexity and generalized convexity play a central role in mathematical programming for duality results and in order to characterize the solutions set. In this paper, taking in mind Craven's notion of K-invexity function (when K is a cone in
\mathbb{R}^n
R
n
) and Martin's notion of Karush-Kuhn-Tucker invexity (hereafter KKT-invexity), we define new notions of generalized convexity for a multiobjective problem with conic constraints. These new notions are both necessary and sufficient to ensure every Karush-Kuhn-Tucker point is a solution. The study of the solutions is also done through the solutions of an associated scalar problem. A Mond-Weir type dual problem is formulated and weak and strong duality results are provided. The notions and results that exist in the literature up to now are particular instances of the ones presented here.
We extend the scalar concept of strong convex function of order k due to G. H. Lin and M. Fukushima ["Some exact penalty results for nonlinear programs and mathematical programs with equilibrium constraints", J. Optim. Theory Appl. 118 (2003) 67–80] to a vector-valued function, by considering a partial order given by a...
C. Gutiérrez, B. Jiménez, V. Novo· Journal of Convex Analysis· 0 citations
This paper investigates higher-order optimality conditions for properly efficient solutions of $C^{1}$ multiobjective optimization problems with inequality constraints. By employing generalized radial directional derivatives, we introduce a higher-order Robinson-type constraint qualification and discuss its relationshi...
C. M. Nguyen, B. X. D. Nguyen, T. M. Nguyen· Reserche operationelle· 0 citations
Necessary conditions of optimality are presented for weakly efficient solutions to multiobjective minimization problems with inequality-type constraints. These conditions are applied when the constraints do not necessarily satisfy any regularity assumptions and they are based on the concept of 2-regularity introduced b...
B. Hernández-Jiménez, M. Rojas-Medar, R. Osuna-Gómez et al.· Journal of Convex Analysis· 0 citations
We study some second-order optimality conditions in terms of second-order Mordukhovich's subdifferentials for the weak efficiency of
C^1
C
1
-smooth robustly quasiconvex multiobjective programming problem with set, inequality and equality constraints. We provide some second-order generalized c...
S. Tran, Hang Dieu Dinh· Journal of Convex Analysis· 0 citations
This work focuses on approximate proper solutions of vector optimization problems. A concept of Henig approximate proper efficiency is introduced and analyzed from several points of view. First, its main properties are stated and the limit behavior in multiobjective problems of the whole Henig approximate proper effici...
C. Gutiérrez, L. Huerga, B. Jiménez et al.· Journal of Convex Analysis· 9 citations· ⚡3
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
