Solving mathematical programs with fuzzy equilibrium constraints

Authors:
Cheng-Feng Hu;Fung-Bao Liu
Affiliations:
I-Shou University, Department of Industrial Engineering and Management, Ta-Hsu, Kaohsiung 840, Taiwan;I-Shou University, Department of Mechanical and Automation Engineering, Ta-Hsu, Kaohsiung 840, Taiwan
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

This work deals with mathematical programs with fuzzy equilibrium constraints. It shows that solving the fuzzy MPEC is equivalent to solving a fuzzy complementarity constrained optimization problem. By using the tolerance approach, we show that the fuzzy complementarity constrained optimization problem can be converted to a regular nonlinear programming problem. A new smoothing approach based on entropic regularization is developed for solving the resulting optimization problem. Numerical examples are also included to illustrate the solution procedure.