Nonconvex scalarization in set optimization with set-valued maps
نویسندگان
چکیده
منابع مشابه
Generalized Algorithm of Tchebyshev Scalarization for Set-Valued Maps
The aim of this paper is to investigate several inherited properties of convexity for set-valued maps and develop computational procedure based on such inherited properties. In this paper, we introduced two types of characteristic functions by using Tchebyshev scalarization, and defined four types of scalarization functions to characterize the images of set-valued maps.
متن کاملStructure of the Fixed Point of Condensing Set-Valued Maps
In this paper, we present structure of the fixed point set results for condensing set-valued map. Also, we prove a generalization of the Krasnosel'skii-Perov connectedness principle to the case of condensing set-valued maps.
متن کاملOptimality Conditions for Vector Optimization with Set-Valued Maps
In this paper, we establish a Farkas-Minkowski type alternative theorem under the supposition of nearly semiconvexlike set-valued maps. Based on the alternative theorem and some other lemmas, we present necessary optimality conditions and sufficient optimality conditions for set-valued vector optimization problems with extended inequality constraints in a sense of weak E-minimizers.
متن کاملGeneralized Convex Set-Valued Maps
The aim of this paper is to show that under a mild semicontinuity assumption (the so-called segmentary epi-closedness), the cone-convex (resp. cone-quasiconvex) set-valued maps can be characterized in terms of weak cone-convexity (resp. weak cone-quasiconvexity), i.e. the notions obtained by replacing in the classical definitions the conditions of type ”for all x, y in the domain and for all t ...
متن کاملStrongly convex set-valued maps
We introduce the notion of strongly t-convex set-valued maps and present some properties of it. In particular, a Bernstein–Doetsch and Sierpiński-type theorems for strongly midconvex set-valued maps, as well as a Kuhn-type result are obtained. A representation of strongly t-convex set-valued maps in inner product spaces and a characterization of inner product spaces involving this representatio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2007
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2006.01.033