Discuss On Some Kinds Of Optimization Problems

The main work of this thesis is divided into two parts. In the first part, by using a penalty method, we explore the existence of solutions for a double obstacle problem: first, we rewrite the double obstacle mixed nonlinear complementarity problem into a double obstacle variational inequality problem; second, we construct a sequence of penalty equations related to the variational inequality problem and show that each penalty equation has at least solution; finally, we prove that the solutions of the penal-ty equations are convergent to a solution of variational inequality problem, and we also give an error estimation of solutions. In the second part, having established the existence and uniqueness of solution for a kind of elliptic boundary value problem, we obtain the existence of the optimal solutions of the rearrangement function optimiza-tion problems related to the elliptic boundary value problems.