Open Access

ARTICLE

A Fictitious Time Integration Method (FTIM) for Solving Mixed Complementarity Problems with Applications to Non-Linear Optimization

Chein-Shan Liu¹, Satya N. Atluri²

1 Department of Mechanical and Mechatronic Engineering, Taiwan Ocean University, Keelung, Tai-wan. E-mail: csliu@mail.ntou.edu.tw.
2 Center for Aerospace Research & Education, University of California, Irvine .

Computer Modeling in Engineering & Sciences 2008, 34(2), 155-178. https://doi.org/10.3970/cmes.2008.034.155

Abstract

In this paper we propose a novel method for solving a nonlinear optimization problem (NOP) under multiple equality and inequality constraints. The Kuhn-Tucker optimality conditions are used to transform the NOP into a mixed complementarity problem (MCP). With the aid of (nonlinear complementarity problem) NCP-functions a set of nonlinear algebraic equations is obtained. Then we develop a fictitious time integration method to solve these nonlinear equations. Several numerical examples of optimization problems, the inverse Cauchy problems and plasticity equations are used to demonstrate that the FTIM is highly efficient to calculate the NOPs and MCPs. The present method has some advantages of easy numerical implementation, ease of treating NOPs, and the ease of extension to higher-dimensional NOPs.

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Keywords

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