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A robust superlinearly convergent algorithm for linearly constrained optimization problems under degeneracy

A robust superlinearly convergent algorithm for linearly constrained optimization problems under... In this paper, the problem of minimizing a convex function subject to general linear constraints is considered. An algorithm which is an extension of the method described in [4] is presented. And a new dual simplex procedure with lexicographic scheme is proposed to deal with the degenerative case in the sense that the gradients of active constraints at the iteration point are dependent. Unlike other methods, the new algorithm possesses the following important property that, at any iteration point generated by the algorithm, one can choose a set of the most suitable basis and from it one can drop all constraints which can be relaxed, not only one constraint once. This property will be helpful in decreasing the computation amount of the algorithm. The global convergence and superlinear convergence of this algorithm are proved, without any assumption of linear independence of the gradients of active constraints. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

A robust superlinearly convergent algorithm for linearly constrained optimization problems under degeneracy

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Publisher
Springer Journals
Copyright
Copyright © 1998 by Science Press
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02683819
Publisher site
See Article on Publisher Site

Abstract

In this paper, the problem of minimizing a convex function subject to general linear constraints is considered. An algorithm which is an extension of the method described in [4] is presented. And a new dual simplex procedure with lexicographic scheme is proposed to deal with the degenerative case in the sense that the gradients of active constraints at the iteration point are dependent. Unlike other methods, the new algorithm possesses the following important property that, at any iteration point generated by the algorithm, one can choose a set of the most suitable basis and from it one can drop all constraints which can be relaxed, not only one constraint once. This property will be helpful in decreasing the computation amount of the algorithm. The global convergence and superlinear convergence of this algorithm are proved, without any assumption of linear independence of the gradients of active constraints.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 4, 2007

References