Constraint Qualifications for Vector Optimization Problems in Real Topological Spaces

In this paper, we introduce a series of definitions of generalized affine functions for vector-valued functions by use of “linear set”. We prove that our generalized affine functions have some similar properties to generalized convex functions. We present examples to show that our generalized affine...

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Bibliographic Details
Published in:Axioms Vol. 12; no. 8; p. 783
Main Author: Zeng, Renying
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.08.2023
Subjects:
affine functions
constraint qualifications
convex functions
Duality theorem
generalized affine functions
generalized convex functions
Graphs
Mathematical optimization
Mathematical research
Optimization
real linear topological spaces
Topological spaces
Topology
Canada
ISSN:2075-1680, 2075-1680
Online Access:Get full text
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Summary:In this paper, we introduce a series of definitions of generalized affine functions for vector-valued functions by use of “linear set”. We prove that our generalized affine functions have some similar properties to generalized convex functions. We present examples to show that our generalized affinenesses are different from one another, and also provide an example to show that our definition of presubaffinelikeness is non-trivial; presubaffinelikeness is the weakest generalized affineness introduced in this article. We work with optimization problems that are defined and taking values in linear topological spaces. We devote to the study of constraint qualifications, and derive some optimality conditions as well as a strong duality theorem. Our optimization problems have inequality constraints, equality constraints, and abstract constraints; our inequality constraints are generalized convex functions and equality constraints are generalized affine functions.
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ISSN:2075-1680
2075-1680
DOI:10.3390/axioms12080783