ITM Web Conf.
Volume 24, 2019AMCSE 2018 - International Conference on Applied Mathematics, Computational Science and Systems Engineering
|Number of page(s)||12|
|Published online||01 February 2019|
E-invexity and generalized E-invexity in E-differentiable multiobjective programming
Department of Mathematics, Hadhramout University, Mukalla -P.O. BOX : (50511-50512), Yemen
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In this paper, a new concept of generalized convexity is introduced for not necessarily diﬀerentiable vector optimization problems. For an E-diﬀerentiable function, the concept of E-invexity is introduced as a generalization of the E-diﬀerentiable E-convexity notion. In addition, some properties of E-diﬀerentiable E-invex functions are investigated. Furthermore, the so-called E-Karush-Kuhn-Tucker necessary optimality conditions are established for the considered E-diﬀerentiable vector optimization problems with both inequality and equality constraints. Also, the suﬃciency of the E-Karush-Kuhn-Tucker necessary optimality conditions are proved for such E-diﬀerentiable vector optimization problems in which the involved functions are E-invex and/or generalized E-invex.
Key words: E-invex set / E-invex function / E-diﬀerentiable function / E-Karush-Kuhn-Tucker necessary optimality conditions
Key words: 90C26 / 90C30 / 90C46 / 90C47
© The Authors, published by EDP Sciences, 2019
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