A Smoothing Newton Method For Mathematical Programs With Linear QVI Constraints

Mathematical programs with equilibrium constraints can be viewed as bilevel programming problems with variational inequalities or complementarity constraints which make such problems difficult to deal with.So the study of optimality conditions and algorithms becomes very important.This thesis is devoted to the study of mathematical programs governed by parameter dependent linear quasi-variational inequalities.The necessary optimality conditions for the optimization problem are reformulated as a system of nonsmooth equations.We introduce a smoothing Newton method to solve the equations.By giving the second order sufficient conditions we prove the BD-regularity of the semi-smooth system and so the quadratic convergence of the smoothing Newton method under mild assumptions.We give an application in a class of inverse linear programming problems.Numerical experiments are reported to show that the smoothing Newton method is effective for solving such problems.