A new smoothing Broyden-like method for solving the mixed complementarity problem with a P-0-function

作者：Tang, Jia^*; Liu, Sanyang

来源：Nonlinear Analysis: Real World Applications , 2010, 11(4): 2770-2786.

DOI：10.1016/j.nonrwa.2009.10.002

• Mixed complementarity problem
• Smoothing function
• Genetic algorithm
• Smoothing Broyden-like algorithm
• Global convergence
• Superlinear convergence

A new smoothing Broyden-like algorithm for solving the mixed complementarity problems (denoted by MCP) is proposed in this paper. The algorithm considered here first uses a floating genetic algorithm to quickly calculate superior results, which are close to the precise solution of the equivalent optimization problems for the mixed complementarity problems, and then by taking the results as the initial values in the following smoothing Broyden-like algorithm, which is based on a perturbed mid function and makes use of the line search rule of D.-H. Li (2000) [16], we obtain a satisfactory approximate solution. In addition, the existence and continuity of a smooth path for solving the mixed complementarity problem with a P-0-function are also discussed. The new smoothing Broyden-like algorithm combines the advantages of quasi-Newton method of local superlinear convergence and a floating genetic algorithm in group search, and global convergence. Numerical results show that the new method is feasible and effective.

• 出版日期2010-8
• 单位西安电子科技大学