Generalized Hadamard well-posedness for infinite vector optimization problems

Z. Y. Peng; X. J. Long; X. F. Wang; Y. B. Zhao

doi:10.1080/02331934.2017.1349767

Generalized Hadamard well-posedness for infinite vector optimization problems

Z. Y. Peng^*, X. J. Long, X. F. Wang, Y. B. Zhao

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

In this paper, we study the generalized Hadamard well-posedness of infinite vector optimization problems (IVOP). Without the assumption of continuity with respect to the first variable, the upper semicontinuity and closedness of constraint set mappings are established. Under weaker assumptions, sufficient conditions of generalized Hadamard well-posedness for IVOP are obtained under perturbations of both the objective function and the constraint set. We apply our results to the semi-infinite vector optimization problem and the semi-infinite multi-objective optimization problem.

Original language	English
Pages (from-to)	1563-1575
Number of pages	13
Journal	Optimization
Volume	66
Issue number	10
Early online date	12 Jul 2017
DOIs	https://doi.org/10.1080/02331934.2017.1349767
Publication status	Published - 3 Oct 2017

Keywords

C-upper semicontinuous
cusco
efficient solution
generalized Hadamard well-posedness
Infinite vector optimization problem
semistrictly K-quasiconvex

ASJC Scopus subject areas

Control and Optimization
Management Science and Operations Research
Applied Mathematics

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title = "Generalized Hadamard well-posedness for infinite vector optimization problems",

abstract = "In this paper, we study the generalized Hadamard well-posedness of infinite vector optimization problems (IVOP). Without the assumption of continuity with respect to the first variable, the upper semicontinuity and closedness of constraint set mappings are established. Under weaker assumptions, sufficient conditions of generalized Hadamard well-posedness for IVOP are obtained under perturbations of both the objective function and the constraint set. We apply our results to the semi-infinite vector optimization problem and the semi-infinite multi-objective optimization problem.",

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T1 - Generalized Hadamard well-posedness for infinite vector optimization problems

AU - Peng, Z. Y.

AU - Long, X. J.

AU - Wang, X. F.

AU - Zhao, Y. B.

PY - 2017/10/3

Y1 - 2017/10/3

N2 - In this paper, we study the generalized Hadamard well-posedness of infinite vector optimization problems (IVOP). Without the assumption of continuity with respect to the first variable, the upper semicontinuity and closedness of constraint set mappings are established. Under weaker assumptions, sufficient conditions of generalized Hadamard well-posedness for IVOP are obtained under perturbations of both the objective function and the constraint set. We apply our results to the semi-infinite vector optimization problem and the semi-infinite multi-objective optimization problem.

AB - In this paper, we study the generalized Hadamard well-posedness of infinite vector optimization problems (IVOP). Without the assumption of continuity with respect to the first variable, the upper semicontinuity and closedness of constraint set mappings are established. Under weaker assumptions, sufficient conditions of generalized Hadamard well-posedness for IVOP are obtained under perturbations of both the objective function and the constraint set. We apply our results to the semi-infinite vector optimization problem and the semi-infinite multi-objective optimization problem.

KW - C-upper semicontinuous

KW - cusco

KW - efficient solution

KW - generalized Hadamard well-posedness

KW - Infinite vector optimization problem

KW - semistrictly K-quasiconvex

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U2 - 10.1080/02331934.2017.1349767

DO - 10.1080/02331934.2017.1349767

M3 - Article

AN - SCOPUS:85023160255

SN - 0233-1934

VL - 66

SP - 1563

EP - 1575

JO - Optimization

JF - Optimization

IS - 10

ER -

Generalized Hadamard well-posedness for infinite vector optimization problems

Abstract

Keywords

ASJC Scopus subject areas

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