Acta Mathematica Vietnamica
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AN INVARIANT PROPERTY OF INVEX FUNCTIONS AND APPLICATIONS
DO VAN LUU, NGUYEN XUAN HA
Abstract
Under directional differentiability assumptions, we prove that the minimum or the maximum of a finite family of invex functions is again an invex function. This invariant property of the invex functions is used to obtain first-order optimality conditions for a class of optimization problems.