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论文类型：期刊论文

发表时间：2010-05-15

发表刊物：Workshop on Iterative Methods and Preconditioning Techniques

收录刊物：SCIE、EI、CPCI-S、Scopus

卷号：216

期号：6

页面范围：1868-1879

ISSN号：0096-3003

关键字：Minimax problem; Truncated aggregate function; Stabilized Newton method

摘要：Aggregate function is a useful smoothing function to the max-function of some smooth functions and has been used to solve minimax problems, linear and nonlinear programming, generalized complementarity problems, etc. The aggregate function is a single smooth but complex function, its gradient and Hessian calculations are time-consuming. In this paper, a truncated aggregate smoothing stabilized Newton method for solving minimax problems is presented. At each iteration, only a small subset of the components in the max-function are aggregated, hence the number of gradient and Hessian calculations is reduced dramatically. The subset is adaptively updated with some truncating criterions, concerning only with computation of function values and not their gradients or Hessians, to guarantee the global convergence and, for the inner iteration, locally quadratic convergence with as few computational cost as possible. Numerical results show the efficiency of the proposed algorithm. (C) 2009 Elsevier Inc. All rights reserved.