A New Trust-Region Algorithm for Finite Minimax
Fusheng Wang 1, Chuanlong Wang 1, Li Wang 21 Department of Mathematics, Taiyuan Normal University, Taiyuan 030012, China
2 Department of Mathematics, University of California, San Diego, USA
Received 2010-10-30 Accepted 2011-7-29
Available online 2012-5-7
In this paper, a new trust region algorithm for minimax optimization problems is proposed, which solves only one quadratic subproblem based on a new approximation model at each iteration. The approach is different with the traditional algorithms that usually require to solve two quadratic subproblems. Moreover, to avoid Maratos effect, the nonmonotone strategy is employed. The analysis shows that, under standard conditions, the algorithm has global and superlinear convergence. Preliminary numerical experiments are conducted to show the effiency of the new method.
Key words: Trust-region methods, Minimax optimization, Nonmonotone strategy, Global convergence, Superlinear convergence.
AMS subject classifications: 90C47, 49K35.
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