Regularity and convexity properties of optimal value functions in parametric programming

Choo and Chew initiated a study of optimal value functions in parametric programming as composition of objective function and point-to-set mappings which define the constrained sets. In the present work more general objective functions in the present context are studied, such as minimax problems which are formed in the setting of parametric programming. Sufficiency condition for the common regularity properties of optimal value functions for the new kind of objective functions are studied. Further the present study also includes the convexity properties of the optimal value functions with respect to the parameter. An attempt is made to study most generalized kind of convexity in the present context. At the end some examples of a program are given where the optimal value function is a generalized convex function of its parameter.