Indexed by:期刊论文

Date of Publication:2010-05-15

Journal:Workshop on Iterative Methods and Preconditioning Techniques

Included Journals:SCIE、EI、CPCI-S、Scopus

Volume:216

Issue:6

Page Number:1868-1879

ISSN No.:0096-3003

Key Words:Minimax problem; Truncated aggregate function; Stabilized Newton method

Abstract: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.