Optimality Conditions And Algorithm For Multiobjective Optimization Problems With Variational Inequality Constraints

Multiobjective optimization problems with equilibrium constraints is the objective function is vector valued function, in its constraint conditions, in addition to the equality and inequality constraints, also contains equilibrium constraints, in this paper, the equilibrium constraints that we discussed is variational inequality constraints. Homotopy method(also be called serial continuation method) is developed from1970s, it is a important kind of big range convergence method and it ues for solving mathematics problems.In this paper we study the optimality conditions and algorithm for multiobjective optimization problems with variational inequality constraints (MOPVIC). Present a combined homotopy interior point method and a new homotopy interior point method for solving the multiobjective optimization problems with variational inequality constraints, construct the relevant homotopy equation to solve the solution of MOPVIC, and proof the existence of homotopic path and the convergence property of the algorithm.First of all, describe the the source and and research significance of this topic briefly, the research background of multiobjective optimization problems with equilibrium constraints, the research background of homotopy method; the basic thoughts and theory of multiobjective optimization problems with equilibrium constraints, the basic thoughts and theory of homotopy method.Then, present a combined homotopy interior point method for solving the multiobjective optimization problems with variational inequality constraints, given the general model of the problem, then by using the smoothing method, change the problem to a equivalent form of single smooth optimization, construct the relevant homotopy equation, and proof the existence of homotopic path and the convergence property of the algorithm. On the basis of combined homotopy interior point method, present a new homotopy interior point method for solving the multiobjective optimization problems with variational inequality constraints, construct the relevant homotopy equation, and proof the existence of homotopic path and the convergence property of the algorithm.Finally, make a simple research work summarizes and further prospects.