Abstract
In this paper, a new concept of generalized convexity is introduced for (not necessarily) differentiable optimization problem with E-differentiable functions. Namely, for an E-differentiable function, the concept of E-B-invexity is defined. The E-differentiable E-B-invexity notion unify the concepts of convexity, invexity, E-convexity, E-invexity and B-invexity. Further, the sufficiency of the so-called E-Karush-Kuhn–Tucker optimality conditions are established for the considered E-differentiable optimization problem with both inequality and equality constraints under E-B-invexity hypotheses. Moreover, the example of a nonsmooth programming problem with E-differentiable functions is constructed to illustrate the aforesaid results.
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