Optimization over the efficient set using an active constraint approach

In this work the problem of maximizing a nonlinear objective over the set of efficient solutions of a multicriteria linear program is considered. This is a nonlinear program with nonconvex constraints. The approach is to develop an active constraint algorithm which utilizes the fact that the efficient structure in decision space can be associated in a natural way with hyperplanes in the space of objective values. Examples and numerical experience are included.