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 in:SIAM journal on optimization 1994-05, Vol.4 (2), p.331-339
Main Authors: Friedlander, Ana, Martínez, José Mario, Santos, Sandra A.
Format: Article
Language:English
Subjects:
Algorithms
Applied mathematics
Optimization
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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.
ISSN:1052-6234
1095-7189
DOI:10.1137/0804018