2016· Journal of Convex Analysis· Vol 23, pp. 661-690· 9 citations· ⚡ 3 influential· 24 references
Abstract
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 efficient set is deduced. These results show that the introduced concept is suitable to approximate the efficient solution set of the problem. After that, the Henig approximate proper efficient solutions are characterized by linear scalarizations under convexity assumptions, and by ε-subgradients in optimization problems dealing with difference of vector mappings. For this last objective, a notion of ε-subdifferential is introduced and studied, obtaining, in particular, a Moreau-Rockafellar type theorem.
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-Kuh...
B. Hernández-Jiménez, R. Osuna-Gómez, M. Rojas-Medar· Journal of Convex Analysis· 0 citations
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
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 consider optimization problems for a class of convex functions on H × H introduced by Simon Fitzpatrick, where H is a real Hilbert space. We show that the minimization problem of Fitzpatrick functions can be transformed from solving of the correspondent differential inclusions (d.i) on H × H, to solving simplified d...
I. Raykov, M. Nashed· Journal of Convex Analysis· 0 citations
In this paper, we examine robust optimality and solution existence for a multiobjective nonsmooth optimization problem involving data uncertainty. To this end, we first introduce the concept of an extended tangency variety associated with the feasible set and a tangency value set for the corresponding robust multiobj...
Li-Guo Jiao, Hung Canh Nguyen, Thai Doan Chuong· Annals of Operations Researc...· 0 citations
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