generalized convexities
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2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Nazih Abderrazzak Gadhi ◽  
Fatima Zahra Rahou

<p style='text-indent:20px;'>In this work, we are concerned with a fractional multiobjective optimization problem <inline-formula><tex-math id="M1">\begin{document}$ (P) $\end{document}</tex-math></inline-formula> involving set-valued maps. Based on necessary optimality conditions given by Gadhi et al. [<xref ref-type="bibr" rid="b14">14</xref>], using support functions, we derive sufficient optimality conditions for <inline-formula><tex-math id="M2">\begin{document}$ \left( P\right) , $\end{document}</tex-math></inline-formula> and we establish various duality results by associating the given problem with its Mond-Weir dual problem <inline-formula><tex-math id="M3">\begin{document}$ \left( D\right) . $\end{document}</tex-math></inline-formula> The main tools we exploit are convexificators and generalized convexities. Examples that illustrates our findings are also given.</p>


Kybernetika ◽  
2017 ◽  
pp. 383-393 ◽  
Author(s):  
Susana Díaz ◽  
Esteban Induráin ◽  
Vladimír Janiš ◽  
Juan Vicente Llinares ◽  
Susana Montes

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Vasile Preda

We consider an interval-valued multiobjective problem. Some necessary and sufficient optimality conditions for weak efficient solutions are established under new generalized convexities with the tool-right upper-Dini-derivative, which is an extension of directional derivative. Also some duality results are proved for Wolfe and Mond-Weir duals.


Author(s):  
Adil Bagirov ◽  
Napsu Karmitsa ◽  
Marko M. Mäkelä

Filomat ◽  
2013 ◽  
Vol 27 (5) ◽  
pp. 899-908 ◽  
Author(s):  
Dehui Yuan ◽  
Xiaoling Liu

In this paper, we give some new generalized convexities with the tool-right upper-Dini-derivative which is an extension of directional derivative. Next, we establish not only Karush-Kuhn-Tucker necessary but also sufficient optimality conditions for mathematical programming involving new generalized convex functions. In the end, weak, strong and converse duality results are proved to relate weak Pareto (efficient) solutions of the multi-objective programming problems (VP), (MVD) and (MWD).


2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Xiaoling Liu ◽  
D. H. Yuan

We firstly construct a concrete semi-invex set which is not invex. Basing on concept of semi-invex set, we introduce some kinds of generalized convex functions, which include semi-(B,G)-preinvex functions, strictly semi-(B,G)-preinvex functions and explicitly semi-(B,G)-preinvex functions. Moreover, we establish relationships between our new generalized convexity and generalized convexity introduced in the literature. With these relationships and the well-known results pertaining to common generalized convexity, we obtain results for our new generalized convexities. We extend the existing results in the literature.


2006 ◽  
Vol 321 (2) ◽  
pp. 675-690 ◽  
Author(s):  
Dehui Yuan ◽  
Altannar Chinchuluun ◽  
Xiaoling Liu ◽  
Panos M. Pardalos

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