An inner approximation method for optimization over the weakly efficient set

In this paper, we consider an optimization problem which aims to minimize a convex function over the weakly efficient set of a multiobjective programm ing problem. To solve such a problem, we propose an inner approximation alg orithm, in which two kinds of convex subproblems are solved successively. T hese convex subproblems are fairly easy to solve and therefore the proposed algorithm is practically useful. The algorithm always terminates after fin itely many iterations by compromising the weak efficiency to a multiobjecti ve programming problem. Moreover, for a subproblem which is solved at each iteration of the algorithm, we suggest a procedure for eliminating redundan t constraints.