Version 1
: Received: 15 September 2023 / Approved: 19 September 2023 / Online: 20 September 2023 (04:51:56 CEST)
How to cite:
Zeng, R. Constraint Qualifications for Vector Optimization Problemsin Real Topological Spaces. Preprints2023, 2023091330. https://doi.org/10.20944/preprints202309.1330.v1
Zeng, R. Constraint Qualifications for Vector Optimization Problemsin Real Topological Spaces. Preprints 2023, 2023091330. https://doi.org/10.20944/preprints202309.1330.v1
Zeng, R. Constraint Qualifications for Vector Optimization Problemsin Real Topological Spaces. Preprints2023, 2023091330. https://doi.org/10.20944/preprints202309.1330.v1
APA Style
Zeng, R. (2023). Constraint Qualifications for Vector Optimization Problemsin Real Topological Spaces. Preprints. https://doi.org/10.20944/preprints202309.1330.v1
Chicago/Turabian Style
Zeng, R. 2023 "Constraint Qualifications for Vector Optimization Problemsin Real Topological Spaces" Preprints. https://doi.org/10.20944/preprints202309.1330.v1
Abstract
. In this paper, we introduce a series of definitions of generalized affine functions for vector-valued functions. We prove that our generalized affine functions have some similar properties with 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 constrains and abstract constraints; our inequality constraints are generalized convex functions and equality constraints are generalized affine functions.
Keywords
real linear topological spaces; affine functions; generalized affine functions; convex functions; generalized convex functions; constraint qualifications
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
