Generalized Minimax Programming with Nondifferentiable (G,β)-Invexity release_n5d2rdzxyzfmvjj2tosz3ide4i

Abstract

We consider the generalized minimax programming problem (P) in which functions are locally Lipschitz (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mrow><mml:mi>β</mml:mi></mml:mrow></mml:math>)-invex. Not only<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:math>-sufficient but also<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:math>-necessary optimality conditions are established for problem (P). With<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M7"><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:math>-necessary optimality conditions and (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M8"><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M9"><mml:mrow><mml:mi>β</mml:mi></mml:mrow></mml:math>)-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.
In application/xml+jats format

Archived Files and Locations