Karush–Kuhn–Tucker optimality conditions and duality for convex semi-infinite programming with multiple interval-valued objective functions

2019 ◽  
Vol 62 (1-2) ◽  
pp. 67-91 ◽  
Author(s):  
Le Thanh Tung
Keyword(s):  
Optimality Conditions ◽  
Objective Functions ◽  
Infinite Programming ◽  
Interval Valued

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 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 Approximate-Karush-Kuhn-Tucker Conditions and Interval Valued Vector Variational Inequalities

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Optimality Conditions ◽  
Optimization Problems ◽  
Vector Variational Inequality ◽  
Vector Variational Inequalities ◽  
Variational Inequality Problems ◽  
Objective Functions ◽  
Interval Valued

This Article deals with the Approximate Karush-Kuhn-Tucker (AKKT) optimality conditions for interval valued multiobjective function as a generalization of Karush-Kuhn-Tucker optimality conditions. Further, we establish relationship between vector variational inequality problems and multiobjective interval valued optimization problems under the assumption of LU−convex smooth and nonsmooth objective functions.

Optimization of the mathematical programming and applications

2021 ◽  
Vol 2 (5) ◽  
pp. 7902-7911
Author(s):  
Johnny Moisés Valverde Montoro ◽  
Milton Milciades Cortez Gutiérrez ◽  
Hernán Oscar Cortez Gutiérrez
Keyword(s):  
Mathematical Programming ◽  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Optimization Problems ◽  
Kkt Conditions ◽  
Objective Functions ◽  
Multiobjective Optimization Problems ◽  
Interval Valued

The present investigation responds to the need to solve optimization problems with optimality conditions. The KKT conditions are considered for multiobjective optimization problems with interval-valued objective functions.

scholarly journals Erratum to " 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 ◽  
Operations Research ◽  
Additional Condition ◽  
Strict Inequality ◽  
Interval Order ◽  
Infinite Programming ◽  
Definition Of ◽  
Interval Valued

This note corrects an error in our paper RAIRO-Operations Research /doi.org/10.1051/ro/2020066 as we should drop the expression ”with at least one strict inequality” in the definition of interval order in Section 2. Instead of proposing this short amendment, the authors of RAIRO-Operations Research doi.org/10.1051/ro/2020107 gave a proposition that requires an additional condition on the constraint functions. However, we claim that all the results of our paper are correct once the modification above is done.

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