Abstract convexity for nonconvex optimization duality

Angelia Nedich, A. Ozdaglar, A. Rubinov

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

In this article, we use abstract convexity results to study augmented dual problems for (nonconvex) constrained optimization problems. We consider a nonincreasing function f that is lower semicontinuous at 0 and establish its abstract convexity at 0 with respect to a set of elementary functions defined by nonconvex augmenting functions. We consider three different classes of augmenting functions: nonnegative augmenting functions, bounded-below augmenting functions, and unbounded augmenting functions. We use the abstract convexity results to study augmented optimization duality without imposing boundedness assumptions.

Original languageEnglish (US)
Pages (from-to)655-674
Number of pages20
JournalOptimization
Volume56
Issue number5-6
DOIs
StatePublished - Oct 2007
Externally publishedYes

Fingerprint

Abstract Convexity
Nonconvex Optimization
Duality
Elementary Functions
Lower Semicontinuous
Dual Problem
Constrained Optimization Problem
Constrained optimization
Convexity
Boundedness
Non-negative
Optimization

Keywords

  • Abstract convexity
  • Augmenting functions
  • Duality
  • Nonconvex optimization

ASJC Scopus subject areas

  • Applied Mathematics
  • Control and Optimization
  • Management Science and Operations Research

Cite this

Abstract convexity for nonconvex optimization duality. / Nedich, Angelia; Ozdaglar, A.; Rubinov, A.

In: Optimization, Vol. 56, No. 5-6, 10.2007, p. 655-674.

Research output: Contribution to journalArticle

Nedich, Angelia ; Ozdaglar, A. ; Rubinov, A. / Abstract convexity for nonconvex optimization duality. In: Optimization. 2007 ; Vol. 56, No. 5-6. pp. 655-674.
@article{2edc1a6dc33d4fc985ff593018adc9bb,
title = "Abstract convexity for nonconvex optimization duality",
abstract = "In this article, we use abstract convexity results to study augmented dual problems for (nonconvex) constrained optimization problems. We consider a nonincreasing function f that is lower semicontinuous at 0 and establish its abstract convexity at 0 with respect to a set of elementary functions defined by nonconvex augmenting functions. We consider three different classes of augmenting functions: nonnegative augmenting functions, bounded-below augmenting functions, and unbounded augmenting functions. We use the abstract convexity results to study augmented optimization duality without imposing boundedness assumptions.",
keywords = "Abstract convexity, Augmenting functions, Duality, Nonconvex optimization",
author = "Angelia Nedich and A. Ozdaglar and A. Rubinov",
year = "2007",
month = "10",
doi = "10.1080/02331930701617379",
language = "English (US)",
volume = "56",
pages = "655--674",
journal = "Optimization",
issn = "0233-1934",
publisher = "Taylor and Francis Ltd.",
number = "5-6",

}

TY - JOUR

T1 - Abstract convexity for nonconvex optimization duality

AU - Nedich, Angelia

AU - Ozdaglar, A.

AU - Rubinov, A.

PY - 2007/10

Y1 - 2007/10

N2 - In this article, we use abstract convexity results to study augmented dual problems for (nonconvex) constrained optimization problems. We consider a nonincreasing function f that is lower semicontinuous at 0 and establish its abstract convexity at 0 with respect to a set of elementary functions defined by nonconvex augmenting functions. We consider three different classes of augmenting functions: nonnegative augmenting functions, bounded-below augmenting functions, and unbounded augmenting functions. We use the abstract convexity results to study augmented optimization duality without imposing boundedness assumptions.

AB - In this article, we use abstract convexity results to study augmented dual problems for (nonconvex) constrained optimization problems. We consider a nonincreasing function f that is lower semicontinuous at 0 and establish its abstract convexity at 0 with respect to a set of elementary functions defined by nonconvex augmenting functions. We consider three different classes of augmenting functions: nonnegative augmenting functions, bounded-below augmenting functions, and unbounded augmenting functions. We use the abstract convexity results to study augmented optimization duality without imposing boundedness assumptions.

KW - Abstract convexity

KW - Augmenting functions

KW - Duality

KW - Nonconvex optimization

UR - http://www.scopus.com/inward/record.url?scp=35148815254&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35148815254&partnerID=8YFLogxK

U2 - 10.1080/02331930701617379

DO - 10.1080/02331930701617379

M3 - Article

AN - SCOPUS:35148815254

VL - 56

SP - 655

EP - 674

JO - Optimization

JF - Optimization

SN - 0233-1934

IS - 5-6

ER -