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We consider the generalized minimax programming problem (P) in which functions are locally Lipschitz (G,β)-invex. Not onlyG-sufficient but alsoG-necessary optimality conditions are established for problem (P). WithG-necessary optimality conditions and (G,β)-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.doi:10.1155/2013/854125 fatcat:n5d2rdzxyzfmvjj2tosz3ide4i