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.

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.

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 On Nonsmooth Semi-Infinite Minimax Programming Problem with(Φ,ρ)-Invexity

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
X. L. Liu ◽  
G. M. Lai ◽  
C. Q. Xu ◽  
D. H. Yuan
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Necessary Optimality Conditions ◽  
Duality Theorems ◽  
Converse Duality ◽  
Minimax Programming ◽  
Carathéodory’S Theorem

We are interested in a nonsmooth minimax programming Problem (SIP). Firstly, we establish the necessary optimality conditions theorems for Problem (SIP) when using the well-known Caratheodory's theorem. Under the Lipschitz(Φ,ρ)-invexity assumptions, we derive the sufficiency of the necessary optimality conditions for the same problem. We also formulate dual and establish weak, strong, and strict converse duality theorems for Problem (SIP) and its dual. These results extend several known results to a wider class of problems.

The Karush–Kuhn–Tucker conditions for multiple objective fractional interval valued optimization problems

2020 ◽  
Vol 54 (4) ◽  
pp. 1161-1188
Author(s):  
Indira P. Debnath ◽  
Shiv K. Gupta
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Pareto Optimality ◽  
Optimization Problems ◽  
Solution Concept ◽  
Multiple Objective ◽  
Clear Understanding ◽  
Interval Valued

In this article, we focus on a class of a fractional interval multivalued programming problem. For the solution concept, LU-Pareto optimality and LS-Pareto, optimality are discussed, and some nontrivial concepts are also illustrated with small examples. The ideas of LU-V-invex and LS-V-invex for a fractional interval problem are introduced. Using these invexity suppositions, we establish the Karush–Kuhn–Tucker optimality conditions for the problem assuming the functions involved to be gH-differentiable. Non-trivial examples are discussed throughout the manuscript to make a clear understanding of the results established. Results obtained in this paper unify and extend some previously known results appeared in the literature.

scholarly journals Optimality Conditions for Nonsmooth Generalized Semi-Infinite Programs

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Zhangyou Chen ◽  
Zhe Chen
Keyword(s):  
Optimality Conditions ◽  
Parametric Optimization ◽  
Necessary Optimality Conditions ◽  
Generalized Differentiation ◽  
Value Functions ◽  
Infinite Programming

We consider a class of nonsmooth generalized semi-infinite programming problems. We apply results from parametric optimization to the lower level problems of generalized semi-infinite programming problems to get estimates for the value functions of the lower level problems and thus derive necessary optimality conditions for generalized semi-infinite programming problems. We also derive some new estimates for the value functions of the lower level problems in terms of generalized differentiation and further obtain the necessary optimality conditions.

scholarly journals Variational Analysis in Semi-Infinite and Infinite Programming, II: Necessary Optimality Conditions

2010 ◽  
Vol 20 (6) ◽  
pp. 2788-2806 ◽  
Author(s):  
M. J. Cánovas ◽  
M. A. López ◽  
B. S. Mordukhovich ◽  
J. Parra
Keyword(s):  
Optimality Conditions ◽  
Variational Analysis ◽  
Necessary Optimality Conditions ◽  
Infinite Programming
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