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2014 An Approximate Proximal Bundle Method to Minimize a Class of Maximum Eigenvalue Functions
Wei Wang, Lingling Zhang, Miao Chen, Sida Lin
J. Appl. Math. 2014: 1-7 (2014). DOI: 10.1155/2014/893765

Abstract

We present an approximate nonsmooth algorithm to solve a minimization problem, in which the objective function is the sum of a maximum eigenvalue function of matrices and a convex function. The essential idea to solve the optimization problem in this paper is similar to the thought of proximal bundle method, but the difference is that we choose approximate subgradient and function value to construct approximate cutting-plane model to solve the above mentioned problem. An important advantage of the approximate cutting-plane model for objective function is that it is more stable than cutting-plane model. In addition, the approximate proximal bundle method algorithm can be given. Furthermore, the sequences generated by the algorithm converge to the optimal solution of the original problem.

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Wei Wang. Lingling Zhang. Miao Chen. Sida Lin. "An Approximate Proximal Bundle Method to Minimize a Class of Maximum Eigenvalue Functions." J. Appl. Math. 2014 1 - 7, 2014. https://doi.org/10.1155/2014/893765

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07131950
MathSciNet: MR3240640
Digital Object Identifier: 10.1155/2014/893765

Rights: Copyright © 2014 Hindawi

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