Smooth representations of optimal solution sets of piecewise linear parametric multiobjective programs

In this chapter, we investigate the smooth representation of the (weakly) efficient solution set of a piecewise linear parametric multiobjective program. We show that if the data of a piecewise linear multiobjective program are smooth functions of a parameter then the (weakly) efficient solution set of the problem can be locally represented as a union of finitely many polyhedra whose vertices and directions are smooth functions of the parameter.Department of Applied Mathematic