Generalized Minimax Programming with Nondifferentiable (G, β)-Invexity

Abstract

We consider the generalized minimax programming problem (P) in which functions are locally Lipschitz ($G$, $\beta$)-invex. Not only $G$-sufficient but also $G$-necessary optimality conditions are established for problem (P). With $G$-necessary optimality conditions and ($G$, $\beta$)-invexity on hand, we construct dual problem (DI) for the primal one (P) and prove duality results between problems (P) and (DI). These results extend several known results to a wider class of programs.