Multiobjective Semi-infinite Optimization: Convexification and Properly Efficient Points

This chapter deals with nonconvex semi-infinite optimization problems that are defined by finitely many objective functions and infinitely many inequality constraints in a finite-dimensional space. Under the reduction approach, it is shown that locally around an efficient point this problem can be transformed equivalently in such a way that the Lagrangian of the transformed weighted sum optimization problem becomes locally convex. Consequently, local duality theory and corresponding solution methods can be used after applying this convexification procedure. Furthermore, the strong relationship between properly efficient points of both the original and the transformed problems is discussed.