Solving implicit mathematical programs with fuzzy variational inequality constraints based on the method of centres with entropic regularization

摘要

The purpose of this paper is to consider a class of mathematical programs with fuzzy implicit variational inequality constraints in finite dimension real spaces. By using the "tolerance approach" and the fuzzy set theory, we also show that solving the fuzzy mathematical program problem with fuzzy implicit variational inequality constraints is equivalent to solving a fuzzy implicit complementarity constrained optimization problem, and the fuzzy implicit complementarity constrained optimization problem can be converted to a regular nonlinear parametric programming problem. Further, a new smoothing approach based on a version of the "method of centres" with entropic regularization for solving the resulting optimization problem and our main results are presented and a numerical example is provided to illustrate our main results applying quasi-Newton line search of MATLAB software.