Karush-Kuhn-Tucker optimality conditions and duality for multiobjective semi-infinite programming with equilibrium constraints

The purpose of this paper is to study multiobjective semi-infinite programming with equilibrium constraints. Firstly, the necessary and sufficient Karush-Kuhn-Tucker optimality conditions for multiobjective semi-infinite programming with equilibrium constraints are established. Then, we formulate types of Wolfe and Mond-Weir dual problems and investigate duality relations under convexity assumptions. Some examples are given to verify our results.

On nondifferentiable minimax semi-infinite programming problems in complex spaces

Georgian Mathematical Journal ◽

10.1515/gmj-2016-0001 ◽

2016 ◽

Vol 23 (3) ◽

pp. 367-380

Author(s):

Anurag Jayswal ◽

Krishna Kummari

Keyword(s):

Optimality Conditions ◽

Programming Problem ◽

Complex Space ◽

Dual Problems ◽

Complex Spaces ◽

Infinite Programming ◽

Primal And Dual Problems ◽

Primal And Dual ◽

AbstractThe purpose of this paper is to study a nondifferentiable minimax semi-infinite programming problem in a complex space. For such a semi-infinite programming problem, necessary and sufficient optimality conditions are established by utilizing the invexity assumptions. Subsequently, these optimality conditions are utilized as a basis for formulating dual problems. In order to relate the primal and dual problems, we have also derived appropriate duality theorems.

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

RAIRO - Operations Research ◽

10.1051/ro/2021145 ◽

2021 ◽

Author(s):

Nazih Abderrazzak Gadhi

Keyword(s):

Optimality Conditions ◽

Equilibrium Constraints ◽

Mathematical Programs ◽

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.

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

RAIRO - Operations Research ◽

10.1051/ro/2018084 ◽

2019 ◽

Vol 53 (5) ◽

pp. 1617-1632 ◽

Cited By ~ 1

Author(s):

Bhawna Kohli

Keyword(s):

Optimality Conditions ◽

Constraint Qualification ◽

Necessary Optimality Conditions ◽

Equilibrium Constraints ◽

Necessary Optimality Condition ◽

First Order ◽

Mathematical Programs ◽

Strong Stationarity ◽

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.

Necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2004.10.032 ◽

2005 ◽

Vol 307 (1) ◽

pp. 350-369 ◽

Cited By ~ 137

Author(s):

Jane J. Ye

Keyword(s):

Optimality Conditions ◽

Equilibrium Constraints ◽

Mathematical Programs ◽

Lagrange duality and saddle point optimality conditions for semi-infinite mathematical programming problems with equilibrium constraints

Yugoslav journal of operations research ◽

10.2298/yjor181215014s ◽

2019 ◽

Vol 29 (4) ◽

pp. 433-448

Author(s):

Kunwar Singh ◽

J.K. Maurya ◽

S.K. Mishra

Keyword(s):

Mathematical Programming ◽

Saddle Point ◽

Optimality Conditions ◽

Optimization Problems ◽

Inequality Constraints ◽

Mathematical Programming Problem ◽

Dual Model ◽

Equilibrium Constraints ◽

Convexity Assumptions ◽

Mathematical Programming Problems

In this paper, we consider a special class of optimization problems which contains infinitely many inequality constraints and finitely many complementarity constraints known as the semi-infinite mathematical programming problem with equilibrium constraints (SIMPEC). We propose Lagrange type dual model for the SIMPEC and obtain their duality results using convexity assumptions. Further, we discuss the saddle point optimality conditions for the SIMPEC. Some examples are given to illustrate the obtained results.

Necessary and Sufficient Optimality Conditions in DC Semi-infinite Programming

SIAM Journal on Optimization ◽

10.1137/19m1303320 ◽

2021 ◽

Vol 31 (1) ◽

pp. 837-865

Author(s):

Rafael Correa ◽

M. A. López ◽

Pedro Pérez-Aros

Keyword(s):

Optimality Conditions ◽

Infinite Programming ◽

Invex optimisation problems

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700011679 ◽

1992 ◽

Vol 46 (1) ◽

pp. 47-66 ◽

Cited By ~ 24

Author(s):

D.T. Luc ◽

C. Malivert

Keyword(s):

Optimality Conditions ◽

Dual Problems ◽

Invex Set ◽

Duality Property ◽

Wolfe Type Dual ◽

In this paper we extend the concept of invexity to set-valued maps and study vector optimisation problems with invex set-valued data. Necessary and sufficient optimality conditions are established in terms of contingent derivatives. Wolfe type dual problems are constructed via two recently developed approaches which guarantee the zero-gap duality property.