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A Feasible Point Method with Bundle Modification for Nonsmooth Convex Constrained Optimization

A Feasible Point Method with Bundle Modification for Nonsmooth Convex Constrained Optimization In this paper, a bundle modification strategy is proposed for nonsmooth convex constrained minimization problems. As a result, a new feasible point bundle method is presented by applying this strategy. Whenever the stability center is updated, some points in the bundle will be substituted by new ones which have lower objective values and/or constraint values, aiming at getting a better bundle. The method generates feasible serious iterates on which the objective function is monotonically decreasing. Global convergence of the algorithm is established, and some preliminary numerical results show that our method performs better than the standard feasible point bundle method. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

A Feasible Point Method with Bundle Modification for Nonsmooth Convex Constrained Optimization

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-018-0755-9
Publisher site
See Article on Publisher Site

Abstract

In this paper, a bundle modification strategy is proposed for nonsmooth convex constrained minimization problems. As a result, a new feasible point bundle method is presented by applying this strategy. Whenever the stability center is updated, some points in the bundle will be substituted by new ones which have lower objective values and/or constraint values, aiming at getting a better bundle. The method generates feasible serious iterates on which the objective function is monotonically decreasing. Global convergence of the algorithm is established, and some preliminary numerical results show that our method performs better than the standard feasible point bundle method.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Apr 26, 2018

References