Tam, Matthew K.
Published in
Optimization Letters

In this work, we consider a framework for the analysis of iterative algorithms which can be described in terms of a structured set-valued operator. More precisely, at each point in the ambient space, we assume that the value of the operator can be expressed as a finite union of values of single-valued paracontracting operators. Our main result, whi...

Das, K. Nahak, C.
Published in
OPSEARCH

In this paper, we establish the sufficient Karush-Kuhn-Tucker (KKT) optimality conditions for the set-valued fractional programming problem (FP) via contingent epiderivative under ρ-cone convexity. We also study the duality results of parametric (PD), Mond-Weir (MWD), Wolfe (WD) and mixed (MD) types for the problem (FP).

García Castaño, F. Melguizo Padial, M. A.
Published in
Journal of Global Optimization

The aim of this paper is to extend the classical envelope theorem from scalar to vector differential programming. The obtained result allows us to measure the quantitative behaviour of a certain set of optimal values (not necessarily a singleton) characterized to become minimum when the objective function is composed with a positive function, accor...

Azzam-Laouir, Dalila Makhlouf, Amira Thibault, Lionel

This paper is devoted to the study of a perturbed differential inclusion governed by a sweeping process in a Hilbert space. The sweeping process is perturbed by a sum of a single-valued map satisfying a Lipschitz condition and a scalarly upper semicontinuous set-valued map.

Pietrus, Alain

This paper deals with variational inclusions of the form 0 2 f(x) + g(x) K where f is smooth function from a re exive Banach space X into a Banach space Y , g is a Lipschitz function from X into Y and K is a nonempty closed convex cone in the space Y . We show that the previous problem can be solved by an extension of the Zincenko's method which ca...

Piszczek, Magdalena
Published in
Results in Mathematics

We present some applications of the result corresponding to the existence of a unique selection of a set-valued function satisfying inclusions in a single variable to the inclusions in several variables, especially the general linear inclusions or quadratic inclusions.

Sach, Pham Huu Tuan, Le Anh
Published in
Journal of Optimization Theory and Applications

This paper gives sufficient conditions for the upper and lower semicontinuities of the solution mapping of a parametric mixed generalized Ky Fan inequality problem. We use a new scalarizing approach quite different from traditional linear scalarization approaches which, in the framework of the stability analysis of solution mappings of equilibrium ...

Cabuzel, Catherine

Zhou, Z. A. Peng, J. W.
Published in
Journal of Optimization Theory and Applications

In real ordered linear spaces, an equivalent characterization of generalized cone subconvexlikeness of set-valued maps is firstly established. Secondly, under the assumption of generalized cone subconvexlikeness of set-valued maps, a scalarization theorem of set-valued optimization problems in the sense of ϵ-weak efficiency is obtained. Finally, by...

Maeda, Takashi
Published in
Journal of Optimization Theory and Applications

In this paper, we consider constrained optimization problems with set-valued objective maps. First, we define three types of quasi orderings on the set of all non-empty subsets of n-dimensional Euclidean space. Second, by using these quasi orderings, we define the concepts of lower semi-continuity for set-valued maps and investigate their propertie...