On Some Mathematical Programming Problems With Vanishing Constraints

Mathematical programs with vanishing constraints (MPVC) is an interesting and difficult class of optimization problems. This kind of problems arise in certain engineering applications such as optimal topology design problems of mechanical structures. In this project, we shall focus our study for mathematical programming programs with vanishing constraints. Necessary and sufficient optimality criteria will be discussed for MPVC involving convexity assumptions for optimal solution. Wolfe and Mond-Weir type dual models of MPVC will be construct , and duality relations shall be establish between MPVC and its dual models. Moreover, equivalence between the optima of MPVC and the saddle point of its Lagrangian function will be present.