On the computation of an element of Clarke generalized Jacobian for a vector-valued max function☆

Abstract In this paper, we present an algorithm for calculating an element of Clarke generalized Jacobian for a vector-valued max-type function. The algorithm reduces the computational cost of an existing algorithm.

[1]  Patrick T. Harker,et al.  Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications , 1990, Math. Program..

[2]  Jong-Shi Pang,et al.  NE/SQP: A robust algorithm for the nonlinear complementarity problem , 1993, Math. Program..

[3]  Liqun Qi,et al.  A nonsmooth version of Newton's method , 1993, Math. Program..

[4]  P. Neittaanmäki,et al.  Nonsmooth Optimization: Analysis and Algorithms with Applications to Optimal Control , 1992 .

[5]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

[6]  Xiaojun Chen,et al.  A verification method for solutions of nonsmooth equations , 1997, Computing.

[7]  Yan Gao.  Newton methods for solving nonsmooth equations via a new subdifferential , 2001, Math. Methods Oper. Res..

[8]  Marko Mäkelä,et al.  Survey of Bundle Methods for Nonsmooth Optimization , 2002, Optim. Methods Softw..

[9]  Yan Gao,et al.  Convergence analysis of nonsmooth equations for the general nonlinear complementarity problem , 2009 .

[10]  Houyuan Jiang,et al.  A New Nonsmooth Equations Approach to Nonlinear Complementarity Problems , 1997 .

[11]  Ji-Ming Peng,et al.  A non-interior continuation method for generalized linear complementarity problems , 1999, Math. Program..

[12]  Francisco Facchinei,et al.  A Theoretical and Numerical Comparison of Some Semismooth Algorithms for Complementarity Problems , 2000, Comput. Optim. Appl..

[13]  Jong-Shi Pang,et al.  A B-differentiable equation-based, globally and locally quadratically convergent algorithm for nonlinear programs, complementarity and variational inequality problems , 1991, Math. Program..

[14]  Jong-Shi Pang,et al.  Piecewise Smoothness, Local Invertibility, and Parametric Analysis of Normal Maps , 1996, Math. Oper. Res..

[15]  Defeng Sun,et al.  Smoothing Functions and Smoothing Newton Method for Complementarity and Variational Inequality Problems , 2002 .

[16]  Francisco Facchinei,et al.  A semismooth equation approach to the solution of nonlinear complementarity problems , 1996, Math. Program..

[18]  Marek J. Smietanski.  An approximate Newton method for non-smooth equations with finite max functions , 2005, Numerical Algorithms.

[19]  Liqun Qi,et al.  Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations , 1993, Math. Oper. Res..

[20]  Huifu Xu,et al.  New Version of the Newton Method for Nonsmooth Equations , 1997 .

[21]  Huifu Xu,et al.  Approximate Newton Methods for Nonsmooth Equations , 1997 .

[22]  M. Kojima,et al.  EXTENSION OF NEWTON AND QUASI-NEWTON METHODS TO SYSTEMS OF PC^1 EQUATIONS , 1986 .

[23]  Patrick T. Harker,et al.  Newton's method for the nonlinear complementarity problem: A B-differentiable equation approach , 1990, Math. Program..