Regularization methods for optimization problems with probabilistic constraints
type: Item
instance of: scholarly article
title: Regularization methods for optimization problems with probabilistic constraints
zbMATH Open document ID: 1276.90043
author: Gabriela Martinez
author: Darinka Dentcheva
published in: Mathematical Programming. Series A. Series B
publication date: 2013-05-06T00:00:00Z
review text: Considered is the following nonlinear optimization problem with probabilistic constraints: \[ \min f(x) \leqno (1) \text{ subject to }\mathbb{P}[g(x)\geq Y] \geq p,\quad x\in \mathcal{D}, \] where \(f:\mathbb{R}^{n}\rightarrow\mathbb{R}\) is a convex function, \(g:\mathbb{R}^{n}\rightarrow\mathbb{R}^{m}\) is componentwise concave, i.e., \(g_{i}:\mathbb{R}^{n}\rightarrow\mathbb{R}\), \(i=1,\dots ,m\), are concave functions, \(\mathcal{D}\subseteq\mathbb{R}^{n}\) is a closed convex set, \(Y\) is an \(m\)-dimensional random vector, the symbol \(\mathbb{P}\) denotes the probability, and it is required that \(g\left( x\right) \geq Y\) shall hold with some prescribed probability \(p\in (0,1)\). The authors develop two efficient numerical methods for solving (1) using regularization techniques. Finally, numerical results based on a bond portfolio and a supply-chain optimization are presented.
Mathematics Subject Classification ID: 90C15
Mathematics Subject Classification ID: 49M29
zbMATH DE Number: 6160899
zbMATH Keywords: stochastic programming
zbMATH Keywords: chance constraints
zbMATH Keywords: duality
reviewed by: I. M. Stancu-Minasian
describes a project that uses: PLCP
MaRDI profile type: Publication
full work available at URL: s10107-012-0539-6
OpenAlex ID: W2090364210
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DOI: 10.1007/S10107-012-0539-6
description: scientific article; zbMATH DE number 6160899