Toward Nonquadratic S-Lemma: New Theory and Application in Nonconvex Optimization

Meijia Yang; Shu Wang; Yong Xia

doi:10.1007/s10957-022-02031-0

Toward Nonquadratic S-Lemma: New Theory and Application in Nonconvex Optimization

Meijia Yang
, Shu Wang
, Yong Xia^*

^*Corresponding author for this work

School of Mathematical Sciences

University of Science and Technology Beijing
North China Electric Power University

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

3 Scopus citations

Abstract

We establish a generalized alternative theorem for nonquadratic nonconvex system by unifying S-lemma and convex Farkas lemma. As an application, we reveal hidden convexity of a new family of nonconvex optimization problems that combine generalized trust region subproblem with convex optimization.

Original language	English
Pages (from-to)	353-363
Number of pages	11
Journal	Journal of Optimization Theory and Applications
Volume	194
Issue number	1
DOIs	https://doi.org/10.1007/s10957-022-02031-0
State	Published - Jul 2022

Keywords

Farkas lemma
Hidden convexity
Nonconvex optimization
S-lemma

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10.1007/s10957-022-02031-0

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title = "Toward Nonquadratic S-Lemma: New Theory and Application in Nonconvex Optimization",

abstract = "We establish a generalized alternative theorem for nonquadratic nonconvex system by unifying S-lemma and convex Farkas lemma. As an application, we reveal hidden convexity of a new family of nonconvex optimization problems that combine generalized trust region subproblem with convex optimization.",

keywords = "Farkas lemma, Hidden convexity, Nonconvex optimization, S-lemma",

author = "Meijia Yang and Shu Wang and Yong Xia",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2022",

month = jul,

doi = "10.1007/s10957-022-02031-0",

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T1 - Toward Nonquadratic S-Lemma

T2 - New Theory and Application in Nonconvex Optimization

AU - Yang, Meijia

AU - Wang, Shu

AU - Xia, Yong

PY - 2022/7

Y1 - 2022/7

N2 - We establish a generalized alternative theorem for nonquadratic nonconvex system by unifying S-lemma and convex Farkas lemma. As an application, we reveal hidden convexity of a new family of nonconvex optimization problems that combine generalized trust region subproblem with convex optimization.

AB - We establish a generalized alternative theorem for nonquadratic nonconvex system by unifying S-lemma and convex Farkas lemma. As an application, we reveal hidden convexity of a new family of nonconvex optimization problems that combine generalized trust region subproblem with convex optimization.

KW - Farkas lemma

KW - Hidden convexity

KW - Nonconvex optimization

KW - S-lemma

UR - https://www.scopus.com/pages/publications/85128165525

U2 - 10.1007/s10957-022-02031-0

DO - 10.1007/s10957-022-02031-0

M3 - 文章

AN - SCOPUS:85128165525

SN - 0022-3239

VL - 194

SP - 353

EP - 363

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 1

ER -

Toward Nonquadratic S-Lemma: New Theory and Application in Nonconvex Optimization

Abstract

Keywords

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