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We consider the generalized minimax programming problem (P) in which functions are locally Lipschitz (G, β)-invex. Not only G-sufficient but also G-necessary optimality conditions are established for problem (P). With G-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

journal of applied mathematics

Generalized Minimax Programming with Nondifferentiable (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>β</mml:mi></mml:mrow></mml:math>)-Invexity

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