Saddle problem and optimization problem as an integrated system
type: Item
instance of: scholarly article
title: Saddle problem and optimization problem as an integrated system
zbMATH Open document ID: 1182.90088
DOI: 10.1134/S0081543808060023
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 2009-10-23T00:00:00Z
review text: Considered is a system of optimization problems with one of them being a saddle problem induced by convex programming and the other, an optimization problem on a convex set: \[ p^*,w^*\in \text{ArgSdl}\{f(w)\mid g(w)\leq y^*,\;w\in W_{0}\}, \tag{1} \] \[ y^*\in \text{ArgMax}\{\langle p^*,y\rangle \mid y\in Y\}, \tag{2} \] where \(f(w)\) is a scalar function, \(g(w)\) is a vector function, \(p\) belongs to the positive orthant \(\mathbb R_+^m\), \(W\subset\mathbb R^n\) and \(Y\subset\mathbb R_+^m\) are convex closed sets. It is assumed that \(f(w)\) and all the components of the function \(g(w)\) are convex. The author examines the properties if this system, the sphere of its application and methods for its solution. The convergence of the proposed methods is established.
Mathematics Subject Classification ID: 90C31
Mathematics Subject Classification ID: 90C25
zbMATH DE Number: 5619804
zbMATH Keywords: parametric optimization
zbMATH Keywords: convex programming
author: Anatoliǐ Sergeevich Antipin
reviewed by: I. M. Stancu-Minasian
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5619804