Strong Karush–Kuhn–Tucker optimality conditions for multiobjective semi-infinite programming via tangential subdifferential

2018 ◽  
Vol 52 (4-5) ◽  
pp. 1019-1041 ◽  
Author(s):  
Le Thanh Tung
Keyword(s):  
Optimality Conditions ◽  
Necessary Optimality Conditions ◽  
Efficient Solutions ◽  
Regularity Conditions ◽  
Infinite Programming ◽  
Kkt Optimality Conditions ◽  
Theoretical Results

The main aim of this paper is to study strong Karush–Kuhn–Tucker (KKT) optimality conditions for nonsmooth multiobjective semi-infinite programming (MSIP) problems. By using tangential subdifferential and suitable regularity conditions, we establish some strong necessary optimality conditions for some types of efficient solutions of nonsmooth MSIP problems. In addition to the theoretical results, some examples are provided to illustrate the advantages of our outcomes.

scholarly journals Constraint qualifications in nonsmooth multiobjective optimization problem

Filomat ◽  
2017 ◽  
Vol 31 (3) ◽  
pp. 781-797 ◽  
Author(s):  
Rekha Gupta ◽  
Manjari Srivastava
Keyword(s):  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Optimization Problem ◽  
Constraint Qualifications ◽  
Necessary Optimality Conditions ◽  
Inequality Constraint ◽  
Efficient Solutions ◽  
Equality Constraints ◽  
Regularity Conditions ◽  
Multiobjective Optimization Problem

A multiobjective optimization problem (MOP) with inequality and equality constraints is considered where the objective and inequality constraint functions are locally Lipschitz and equality constraint functions are differentiable. Burachik and Rizvi [J. Optim. Theory Appl. 155, 477-491 (2012)] gave Guignard and generalized Abadie regularity conditions for a differentiable programming problem and derived Karush-Kuhn-Tucker (KKT) type necessary optimality conditions. In this paper, we have defined the nonsmooth versions of Guignard and generalized Abadie regularity conditions given by Burachik and Rizvi and obtained KKT necessary optimality conditions for efficient and weak efficient solutions of (MOP). Further several constraint qualifications sufficient for the above newly defined constraint qualifications are introduced for (MOP) with no equality constraints. Relationships between them are presented and examples are constructed to support the results.

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 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

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.

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