TY - JOUR
T1 - A New Trust-Region Algorithm for Finite Minimax Problem
AU - Wang , Fusheng
AU - Wang , Chuanlong
AU - Wang , Li
JO - Journal of Computational Mathematics
VL - 3
SP - 262
EP - 278
PY - 2012
DA - 2012/06
SN - 30
DO - http://doi.org/10.4208/jcm.1109-m3567
UR - https://global-sci.org/intro/article_detail/jcm/8429.html
KW - Trust-region methods, Minimax optimization, Nonmonotone strategy, Global
convergence, Superlinear convergence.
AB - <p style="text-align: justify;">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 from 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 efficiency of the new method.</p>