New regularity conditions and Fenchel dualities for DC optimization problems involving composite functions

Donghui Fang; Qamrul Hasan Ansari; Jen Chih Yao

doi:10.1080/02331934.2020.1737864

New regularity conditions and Fenchel dualities for DC optimization problems involving composite functions

Donghui Fang, Qamrul Hasan Ansari^*, Jen Chih Yao

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

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

1 Scopus citations

Abstract

We consider the following DC composite optimization problem (P): (Formula presented.) where (Formula presented.) and (Formula presented.) are proper convex functionals defined on locally convex Hausdorff topological vector spaces X and Y respectively, and h is a proper K-convex mapping from X to Y. By using the properties of the epigraph of the conjugate functions, we introduce some new regularity conditions and obtain complete characterizations for weak / strong / stable Fenchel dualities and for zero / stable zero duality gap properties of problem (P).

Original language	English
Pages (from-to)	777-803
Number of pages	27
Journal	Optimization
Volume	70
Issue number	4
DOIs	https://doi.org/10.1080/02331934.2020.1737864
State	Published - 2021

Bibliographical note

Publisher Copyright:
© 2020 Informa UK Limited, trading as Taylor & Francis Group.

Keywords

DC programming
Regularity condition
composite optimization problem
strong duality
zero duality gap property

ASJC Scopus subject areas

Control and Optimization
Management Science and Operations Research
Applied Mathematics

Access to Document

10.1080/02331934.2020.1737864

Cite this

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abstract = "We consider the following DC composite optimization problem (P): (Formula presented.) where (Formula presented.) and (Formula presented.) are proper convex functionals defined on locally convex Hausdorff topological vector spaces X and Y respectively, and h is a proper K-convex mapping from X to Y. By using the properties of the epigraph of the conjugate functions, we introduce some new regularity conditions and obtain complete characterizations for weak / strong / stable Fenchel dualities and for zero / stable zero duality gap properties of problem (P).",

keywords = "DC programming, Regularity condition, composite optimization problem, strong duality, zero duality gap property",

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T1 - New regularity conditions and Fenchel dualities for DC optimization problems involving composite functions

AU - Fang, Donghui

AU - Ansari, Qamrul Hasan

AU - Yao, Jen Chih

PY - 2021

Y1 - 2021

N2 - We consider the following DC composite optimization problem (P): (Formula presented.) where (Formula presented.) and (Formula presented.) are proper convex functionals defined on locally convex Hausdorff topological vector spaces X and Y respectively, and h is a proper K-convex mapping from X to Y. By using the properties of the epigraph of the conjugate functions, we introduce some new regularity conditions and obtain complete characterizations for weak / strong / stable Fenchel dualities and for zero / stable zero duality gap properties of problem (P).

AB - We consider the following DC composite optimization problem (P): (Formula presented.) where (Formula presented.) and (Formula presented.) are proper convex functionals defined on locally convex Hausdorff topological vector spaces X and Y respectively, and h is a proper K-convex mapping from X to Y. By using the properties of the epigraph of the conjugate functions, we introduce some new regularity conditions and obtain complete characterizations for weak / strong / stable Fenchel dualities and for zero / stable zero duality gap properties of problem (P).

KW - DC programming

KW - Regularity condition

KW - composite optimization problem

KW - strong duality

KW - zero duality gap property

UR - https://www.scopus.com/pages/publications/85081745395

U2 - 10.1080/02331934.2020.1737864

DO - 10.1080/02331934.2020.1737864

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EP - 803

JO - Optimization

JF - Optimization

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ER -