Indexed by:期刊论文
Date of Publication:2015-07-01
Journal:JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
Included Journals:SCIE、Scopus
Volume:166
Issue:1
Page Number:257-277
ISSN No.:0022-3239
Key Words:Minimax problem; Nondifferentiable optimization; Sparsity; Large scale; Group update
Abstract:A group update algorithm is presented for solving minimax problems with a finite number of functions, whose Hessians are sparse. The method uses the gradient evaluations as efficiently as possible by updating successively the elements in partitioning groups of the columns of every Hessian in the process of iterations. The chosen direction is determined directly by the nonzero elements of the Hessians in terms of partitioning groups. The local -superlinear convergence of the method is proved, without requiring the imposition of a strict complementarity condition, and the -convergence rate is estimated. Furthermore, two efficient methods handling nonconvex case are given. The global convergence of one method is proved, and the local -superlinear convergence and -convergence rate of another method are also proved or estimated by a novel technique. The robustness and efficiency of the algorithms are verified by numerical tests.
Professor
Supervisor of Doctorate Candidates
Supervisor of Master's Candidates
Gender:Male
Alma Mater:吉林大学
Degree:Doctoral Degree
School/Department:数学科学学院
Discipline:Computational Mathematics. Financial Mathematics and Actuarial Science
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