scholarly journals Optimality conditions for nonsmooth interval-valued and multiobjective semi-infinite programming

2020 ◽  
Author(s):  
Mohsine Jennane ◽  
El Mostafa Kalmoun ◽  
Lahoussine Lafhim
Keyword(s):  
Optimality Conditions ◽  
Optimization Problem ◽  
Constraint Qualification ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Convexity Assumption ◽  
Locally Lipschitz ◽  
Infinite Programming ◽  
Asymptotic Convexity ◽  
Interval Valued

We consider a nonsmooth semi-infinite interval-valued vector programming problem, where the objectives and constraints functions need not to be locally Lipschitz. Using Abadie's constraint qualification and convexificators, we provide  Karush-Kuhn-Tucker necessary optimality conditions by converting the initial problem into a bi-criteria optimization problem. Furthermore, we establish sufficient optimality conditions  under the asymptotic convexity assumption.

scholarly journals Robust Approximate Optimality Conditions for Uncertain Nonsmooth Optimization with Infinite Number of Constraints

Mathematics ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 12 ◽  
Author(s):  
Xiangkai Sun ◽  
Hongyong Fu ◽  
Jing Zeng
Keyword(s):  
Optimality Conditions ◽  
Optimization Problem ◽  
Constraint Qualification ◽  
Optimization Problems ◽  
Optimization Technique ◽  
Optimal Solution ◽  
Sufficient Optimality Conditions ◽  
Convex Constraint ◽  
Approximate Optimality Conditions ◽  
Necessary And Sufficient

This paper deals with robust quasi approximate optimal solutions for a nonsmooth semi-infinite optimization problems with uncertainty data. By virtue of the epigraphs of the conjugates of the constraint functions, we first introduce a robust type closed convex constraint qualification. Then, by using the robust type closed convex constraint qualification and robust optimization technique, we obtain some necessary and sufficient optimality conditions for robust quasi approximate optimal solution and exact optimal solution of this nonsmooth uncertain semi-infinite optimization problem. Moreover, the obtained results in this paper are applied to a nonsmooth uncertain optimization problem with cone constraints.

Necessary and sufficient optimality conditions using convexifactors for mathematical programs with equilibrium constraints

2019 ◽  
Vol 53 (5) ◽  
pp. 1617-1632 ◽  
Author(s):  
Bhawna Kohli
Keyword(s):  
Optimality Conditions ◽  
Constraint Qualification ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Equilibrium Constraints ◽  
Necessary Optimality Condition ◽  
First Order ◽  
Mathematical Programs ◽  
Strong Stationarity ◽  
Necessary And Sufficient

The main aim of this paper is to develop necessary Optimality conditions using Convexifactors for mathematical programs with equilibrium constraints (MPEC). For this purpose a nonsmooth version of the standard Guignard constraint qualification (GCQ) and strong stationarity are introduced in terms of convexifactors for MPEC. It is shown that Strong stationarity is the first order necessary optimality condition under nonsmooth version of the standard GCQ. Finally, notions of asymptotic pseudoconvexity and asymptotic quasiconvexity are used to establish the sufficient optimality conditions for MPEC.

scholarly journals Comments on " Optimality conditions for nonsmooth interval-valued and multiobjective semi-infinite programming"

2021 ◽  
Author(s):  
Nazih Abderrazzak Gadhi ◽  
Aissam Ichatouhane
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Necessary Optimality Conditions ◽  
Infinite Interval ◽  
Critical Response ◽  
Infinite Programming ◽  
Interval Valued

Necessary optimality conditions for a nonsmooth semi-infinite interval-valued vector programming problem are given in the paper by Jennane et all. (RAIRO-Oper. Res. doi: 10.1051/ro/2020066,2020). Having noticed inconsistencies in their paper, Gadhi and Ichatouhane (RAIRO-Oper. Res. doi:10.1051/ro/2020107, 2020) made the necessary corrections and proposed what they considered a more pertinent formulation of their main Theorem. Recently, Jennane et all. (RAIRO-Oper. Res. doi: 10.1051/ro/2020134) have criticised our work. This note is a critical response to this criticism.

Necessary and sufficient optimality conditions for set-valued optimization problems

2011 ◽  
Vol 18 (1) ◽  
pp. 53-66
Author(s):  
Najia Benkenza ◽  
Nazih Gadhi ◽  
Lahoussine Lafhim
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Necessary And Sufficient ◽  
First Time ◽  
Funct Anal

Abstract Using a special scalarization employed for the first time for the study of necessary optimality conditions in vector optimization by Ciligot-Travain [Numer. Funct. Anal. Optim. 15: 689–693, 1994], we give necessary optimality conditions for a set-valued optimization problem by establishing the existence of Lagrange–Fritz–John multipliers. Also, sufficient optimality conditions are given without any Lipschitz assumption.

scholarly journals Sufficient optimality conditions and Mond-Weir duality results for a fractional multiobjective optimization problem

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Nazih Abderrazzak Gadhi ◽  
Fatima Zahra Rahou
Keyword(s):  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Optimization Problem ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Multiobjective Optimization Problem ◽  
Support Functions ◽  
Duality Results ◽  
The Given ◽  
Generalized Convexities

<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>

scholarly journals Necessary optimality conditions for a fractional multiobjective optimization problem

2020 ◽  
Author(s):  
Nazih Abderrazzak Gadhi ◽  
khadija hamdaoui ◽  
mohammed El idrissi ◽  
Fatima zahra Rahou
Keyword(s):  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Optimization Problem ◽  
Constraint Qualification ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Multiobjective Optimization Problem ◽  
Support Functions

In this paper, we are concerned with a fractional multiobjective optimization problem (P). Using support functions together with a generalized Guignard constraint qualification, we give necessary optimality conditions in terms of convexificators and the Karush-Kuhn-Tucker multipliers. Several intermediate optimization problems have been introduced to help us in our investigation.

scholarly journals Optimality conditions for nonsmooth multiobjective bilevel optimization using tangential subdifferentials

2021 ◽  
Author(s):  
Mohsine Jennane ◽  
El Mostafa Kalmoun ◽  
Lhoussain El Fadil
Keyword(s):  
Optimality Conditions ◽  
Bilevel Programming ◽  
Constraint Qualification ◽  
Value Function ◽  
Necessary Optimality Conditions ◽  
Bilevel Optimization ◽  
Bilevel Programming Problem ◽  
Locally Lipschitz ◽  
Upper Level ◽  
The Value Function

In combining the value function approach and tangential subdifferentials, we establish  necessary optimality conditions of  a nonsmooth multiobjective bilevel programming problem under a suitable constraint qualification. The upper level objectives and constraint functions are neither assumed to be necessarily locally Lipschitz nor convex.

scholarly journals A note on the paper "Optimality conditions for nonsmooth interval-valued and multiobjective semi-infinite programming"

2020 ◽  
Author(s):  
Nazih Abderrazzak Gadhi ◽  
Aissam Ichatouhane
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Optimality Condition ◽  
Short Proof ◽  
Necessary Optimality Condition ◽  
Main Result Theorem ◽  
Correct Formulation ◽  
Result Theorem ◽  
Infinite Programming ◽  
Interval Valued

A nonsmooth semi-infinite interval-valued vector programming problem is solved in the paper by Jennane et all. (RAIRO-Oper. Res. doi: 10.1051/ro/2020066, 2020). The necessary optimality condition obtained by the authors, as well as its proof, is false. Some counterexamples are given to refute some results on which the main result (Theorem 4.5) is based. For the convinience of the reader, we correct the faulty in those results, propose a correct formulation of Theorem 4.5 and give also a short proof.

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