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On Nesterov's Approach to Semi-infinite Programming

On Nesterov's Approach to Semi-infinite Programming We generalize Nesterov's construction for the reduction of various classes of semi-infinite programming problems to the semidefinite programming form. In this way, we are able to consider ‘cones of squares’ of real-valued and matrix-valued functions as rather particular cases of a unifying abstract scheme. We also interpret from this viewpoint some results of M. Krein and A. Nudelman. This provides (in a way which probably has not been anticipated by these authors) a very powerful tool for solving various optimization problems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

On Nesterov's Approach to Semi-infinite Programming

Acta Applicandae Mathematicae , Volume 74 (2) – Oct 10, 2004

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References (54)

Publisher
Springer Journals
Copyright
Copyright © 2002 by Kluwer Academic Publishers
Subject
Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1023/A:1020643711475
Publisher site
See Article on Publisher Site

Abstract

We generalize Nesterov's construction for the reduction of various classes of semi-infinite programming problems to the semidefinite programming form. In this way, we are able to consider ‘cones of squares’ of real-valued and matrix-valued functions as rather particular cases of a unifying abstract scheme. We also interpret from this viewpoint some results of M. Krein and A. Nudelman. This provides (in a way which probably has not been anticipated by these authors) a very powerful tool for solving various optimization problems.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Oct 10, 2004

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