Generalized minimax programming with nondifferentiable \((G, \beta)\)-invexity (Q2375696)

Summary: 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.