Optimality conditions for convex problems on intersections of non necessarily convex sets

E. Allevi; R. Riccardi; Juan Enrique Martínez Legaz

doi:10.1007/s10898-019-00849-z

Optimality conditions for convex problems on intersections of non necessarily convex sets

E. Allevi, R. Riccardi, Juan Enrique Martínez Legaz

Department of Economics and Economic History

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

9 Citations (Scopus)

Abstract

We present necessary and sufficient optimality conditions for the minimization of pseudoconvex functions over convex intersections of non necessarily convex sets. To this aim, we use the notion of local normal cone to a closed set at a point, due to Linh and Penot (SIAM J Optim 17:500-510, 2006). The technique we use to obtain the optimality conditions is based on the so called canonical representation of a closed set by means of its associated oriented distance function.

Original language	English
Pages (from-to)	143-155
Number of pages	13
Journal	Journal of Global Optimization
Volume	77
DOIs	https://doi.org/10.1007/s10898-019-00849-z
Publication status	Published - 25 Oct 2019

Keywords

Convex optimization
Nonsmooth optimization
Optimality conditions

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title = "Optimality conditions for convex problems on intersections of non necessarily convex sets",

abstract = "We present necessary and sufficient optimality conditions for the minimization of pseudoconvex functions over convex intersections of non necessarily convex sets. To this aim, we use the notion of local normal cone to a closed set at a point, due to Linh and Penot (SIAM J Optim 17:500-510, 2006). The technique we use to obtain the optimality conditions is based on the so called canonical representation of a closed set by means of its associated oriented distance function.",

keywords = "Convex optimization, Nonsmooth optimization, Optimality conditions",

author = "E. Allevi and R. Riccardi and \{Mart{\'i}nez Legaz\}, \{Juan Enrique\}",

note = "We are grateful to Regina S. Burachik for helpful discussions on the notion of local normal cone. We also thank two anonymous reviewers by their useful corrections and remarks, which helped us to improve the presentation; in particular, one of them provided us with the current simplified proof of Lemma",

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AU - Allevi, E.

AU - Riccardi, R.

AU - Martínez Legaz, Juan Enrique

N1 - We are grateful to Regina S. Burachik for helpful discussions on the notion of local normal cone. We also thank two anonymous reviewers by their useful corrections and remarks, which helped us to improve the presentation; in particular, one of them provided us with the current simplified proof of Lemma

PY - 2019/10/25

Y1 - 2019/10/25

N2 - We present necessary and sufficient optimality conditions for the minimization of pseudoconvex functions over convex intersections of non necessarily convex sets. To this aim, we use the notion of local normal cone to a closed set at a point, due to Linh and Penot (SIAM J Optim 17:500-510, 2006). The technique we use to obtain the optimality conditions is based on the so called canonical representation of a closed set by means of its associated oriented distance function.

AB - We present necessary and sufficient optimality conditions for the minimization of pseudoconvex functions over convex intersections of non necessarily convex sets. To this aim, we use the notion of local normal cone to a closed set at a point, due to Linh and Penot (SIAM J Optim 17:500-510, 2006). The technique we use to obtain the optimality conditions is based on the so called canonical representation of a closed set by means of its associated oriented distance function.

KW - Convex optimization

KW - Nonsmooth optimization

KW - Optimality conditions

UR - https://www.scopus.com/pages/publications/85074397681

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DO - 10.1007/s10898-019-00849-z

M3 - Article

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VL - 77

SP - 143

EP - 155

JO - Journal of Global Optimization

JF - Journal of Global Optimization

ER -

Optimality conditions for convex problems on intersections of non necessarily convex sets

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Keywords

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