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 A note on the paper "Necessary and sufficient optimality conditions using convexifactors for mathematical programs with equilibrium constraints"

2021 ◽  
Author(s):  
Nazih Abderrazzak Gadhi
Keyword(s):  
Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Equilibrium Constraints ◽  
Mathematical Programs ◽  
Necessary And Sufficient

In this work, some counterexamples are given to refute some results in the paper by Kohli (RAIRO-Oper. Res. 53, 1617-1632, 2019). We correct the faulty in some of his results.

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.

scholarly journals Duality and Lagrange multipliers for nonsmooth multiobjective programming

2006 ◽  
Vol 74 (3) ◽  
pp. 369-383 ◽  
Author(s):  
Houchun Zhou ◽  
Wenyu Sun
Keyword(s):  
Optimality Conditions ◽  
Lagrange Multipliers ◽  
Constraint Qualification ◽  
Multiobjective Programming ◽  
Sufficient Optimality Conditions ◽  
Dual Model ◽  
Mixed Duality ◽  
Nonsmooth Multiobjective Programming ◽  
Necessary And Sufficient ◽  
Dual Models

Without any constraint qualification, the necessary and sufficient optimality conditions are established in this paper for nonsmooth multiobjective programming involving generalised convex functions. With these optimality conditions, a mixed dual model is constructed which unifies two dual models. Several theorems on mixed duality and Lagrange multipliers are established in this paper.

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 Generalized convexity in nondifferentiable programming

1984 ◽  
Vol 30 (2) ◽  
pp. 193-218 ◽  
Author(s):  
Bevil M. Glover
Keyword(s):  
Mathematical Programming ◽  
Optimality Conditions ◽  
Programming Problem ◽  
Constraint Qualification ◽  
Generalized Convexity ◽  
Nondifferentiable Programming ◽  
Mathematical Programming Problem ◽  
Sufficient Optimality Conditions ◽  
Cone Constraints ◽  
Necessary And Sufficient

For an abstract mathematical programming problem involving quasidifferentiable cone-constraints we obtain necessary (and sufficient) optimality conditions of the Kuhn-Tucker type without recourse to a constraint qualification. This extends the known results to the non-differentiable setting. To obtain these results we derive several simple conditions connecting various concepts in generalized convexity not requiring differentiability of the functions involved.

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.

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