Results 21 to 30 of about 450,792 (279)

Set-Valued Robust Mappings and Approximatable Mappings

Journal of Mathematical Analysis and Applications, 1994
The second author recently proposed the concept of robustness of sets and functions for weakening the requirement of continuity of the objective functions and constraints in global optimization problems. In this paper the authors propose the concept of lower robustness and of lower approximation for a set-valued mapping and show that any lower ...
Shi, S.Z., Zheng, Q., Zhuang, D.M.
openaire   +1 more source

Necessary and Sufficient Conditions for Set-Valued Maps with Set Optimization

Abstract and Applied Analysis, 2018
Optimality conditions are studied for set-valued maps with set optimization. Necessary conditions are given in terms of S-derivative and contingent derivative.
Abdessamad Oussarhan, Ikram Daidai
doaj   +1 more source

Rough semi-continuous set-valued maps

, 2021
Summary: In this paper, we introduce the concepts of rough semi-continuity and rough continuity of set-valued maps. Then we investigate the question whether these concepts may be characterized differently or not.
AYTAR, Salih, Akcay, Fatma Gecit
openaire   +3 more sources

On the Extensions of Single Valued Continuous and Set Valued Usc Maps [PDF]

, 2001
We show that two main theorems: (1) A regular space Y has a complete sequence if and only if the set valued usco map to Y defined on every dense set D of any space X has an usco extension over a Gδ-set in X containing D. (2) A regular space Y with a
Ikenaga, Shogo, Nitta, Shin-ichi, Yoshioka, Iwao   +2 more
core   +1 more source

Coincidence Point, Best Approximation, and Best Proximity Theorems for Condensing Set-Valued Maps in Hyperconvex Metric Spaces

Fixed Point Theory and Applications, 2009
In hyperconvex metric spaces, we first present a coincidence point theorem for condensing set-valued self-maps. Then we consider the best approximation problem and the best proximity problem for set-valued mappings that are condensing. As an application,
A. Amini-Harandi, A. P. Farajzadeh, D. O'Regan, R. P. Agarwal   +3 more
doaj   +1 more source

Optimality Conditions and Dualities for Robust Efficient Solutions of Uncertain Set-Valued Optimization with Set-Order Relations

Axioms, 2022
In this paper, we introduce a second-order strong subdifferential of set-valued maps, and discuss some properties, such as convexity, sum rule and so on.
Yuwen Zhai, Qilin Wang, Tian Tang
doaj   +1 more source

An inverse mapping theorem for set-valued maps [PDF]

Proceedings of the American Mathematical Society, 1994
We prove that certain Lipschitz properties of the inverse F − 1 {F^{ - 1}} of a set-valued map F are inherited by the map ( f + F ) − 1 {(f + F)^{ - 1}} when f ...
Dontchev, A. L., Hager, W. W.
openaire   +1 more source

On reduction of differential inclusions and Lyapunov stability

, 2019
In this paper, locally Lipschitz, regular functions are utilized to identify and remove infeasible directions from set-valued maps that define differential inclusions.
Dixon, Warren E., Kamalapurkar, Rushikesh, Teel, Andrew R.   +2 more
core   +1 more source

On the Existence of Super Efficient Solutions and Optimality Conditions for Set-Valued Vector Optimization Problems

Mathematics, 2022
In this paper, by using the normal subdifferential and equilibrium-like function we first obtain some properties for K-preinvex set-valued maps. Secondly, in terms of this equilibrium-like function, we establish some sufficient conditions for the ...
Lu-Chuan Ceng, Ching-Feng Wen, Yeong-Cheng Liou   +2 more
doaj   +1 more source

Optimality and duality in set-valued optimization utilizing limit sets

Open Mathematics, 2018
This paper deals with optimality conditions and duality theory for vector optimization involving non-convex set-valued maps. Firstly, under the assumption of nearly cone-subconvexlike property for set-valued maps, the necessary and sufficient optimality ...
Kong Xiangyu, Zhang Yinfeng, Yu GuoLin
doaj   +1 more source