The DC Algorithm For Solving Quadratic Programs With Linear Complementarity Constraints

In this thesis,we study the difference-of-convex approach for quadratic programs with complementarity constraints(QPCC)which is a special kind of Mathematical problems with equilibrium constraints.Mathematical problems with equilibrium constraints are widely used in transportation,optimal pricing and other issues.Due to the existence of complementary constraints,the feasible domain of Mathematical problems with equilibrium constraints is usually non-convex or even non-connected,and the usual constraint specifications at any feasible point are not valid,so some classical algorithms for solving nonlinear programming problems cannot be directly applied to the Mathematical problems with equilibrium constraints.In the second chapter,we study the case under the convex hypothesis,that is,the objective function of QPCC is convex,and the function in the inequality constraint is also convex.In this case,we partially penalize the complementary constraint to the objective function.We study two forms of penalization including non-smooth penalization form and bilinear penalization form.Then we use the DC algorithms to obtain their stationary points and discuss the relationships between stationary points of the two penalty problems and their corresponding original problems.The third chapter is still discussed under the convex hypothesis where we express the complementary constraints as a DC form,and use the generalized DC algorithm to solve the problem.The algorithm is convergent to the weak stationary point of the QPCC under certain conditions.In the fourth chapter,we generalize the contents of the second and third chapters.For the DC problem with linear complementarity constraints,the objective function and the functions in inequality constraints are also DC functions.We use the non-smooth penalty method to partially penalize the complementary constraint to the objective function,and use the generalized DC algorithm to solve the problem.Then we express the complementary constraints as DC form,and use the generalized DC algorithm solves the problem.Chapter 5 is to give some numerical experiments.We present the analysis of numerical experiments and give advice for the further research.