On the Resolution of Linearly Constrained Convex Minimization Problems

The problem of minimizing a twice differentiable convex function $f$ is considered, subject to $Ax = b, x \geq 0$, where $A \in \mathbb{R}^{M \times N} ,M,N$ are large and the feasible region is bounded. It is proven that this problem is equivalent to a "primal-dual" box-constrained proble...

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Bibliographic Details
Published inSIAM journal on optimization Vol. 4; no. 2; pp. 331 - 339
Main Authors Friedlander, Ana, Martínez, José Mario, Santos, Sandra A.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.05.1994
Subjects
Algorithms
Applied mathematics
Optimization
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ISSN1052-6234
1095-7189
DOI10.1137/0804018

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Summary:The problem of minimizing a twice differentiable convex function $f$ is considered, subject to $Ax = b, x \geq 0$, where $A \in \mathbb{R}^{M \times N} ,M,N$ are large and the feasible region is bounded. It is proven that this problem is equivalent to a "primal-dual" box-constrained problem with $2N + M$ variables. The equivalent problem involves neither penalization parameters nor ad hoc multiplier estimators. This problem is solved using an algorithm for bound constrained minimization that can deal with many variables. Numerical experiments are presented.
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ISSN:1052-6234
1095-7189
DOI:10.1137/0804018