A Fictitious Time Integration Method (FTIM) for Solving Mixed Complementarity Problems with Applications to Non-Linear Optimization
Chein-Shan Liu; and Satya N. Atluri

doi:10.3970/cmes.2008.034.155
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 34, No. 2, pp. 155-178, 2008
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Keywords Nonlinear optimization problem, Mixed complementarity problem, NCP-functions, Fictitious time integration method (FTIM)
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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