On nondifferentiable minimax semi-infinite programming problems in complex spaces

2016 ◽  
Vol 23 (3) ◽  
pp. 367-380
Author(s):  
Anurag Jayswal ◽  
Krishna Kummari
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Complex Space ◽  
Sufficient Optimality Conditions ◽  
Dual Problems ◽  
Complex Spaces ◽  
Infinite Programming ◽  
Primal And Dual Problems ◽  
Primal And Dual ◽  
Necessary And Sufficient

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.

scholarly journals Multiobjective duality with ρ−(η,θ)-invexity

2005 ◽  
Vol 2005 (2) ◽  
pp. 175-180 ◽  
Author(s):  
C. Nahak ◽  
S. Nanda
Keyword(s):  
Programming Problem ◽  
Multiobjective Programming ◽  
Efficient Solutions ◽  
Duality Theorems ◽  
Converse Duality ◽  
Dual Problems ◽  
Properly Efficient Solutions ◽  
Multiobjective Programming Problem ◽  
Primal And Dual Problems ◽  
Primal And Dual

Under ρ−(η,θ)-invexity assumptions on the functions involved, weak, strong, and converse duality theorems are proved to relate properly efficient solutions of the primal and dual problems for a multiobjective programming problem.

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

2020 ◽  
pp. 24-24
Author(s):  
Thanh Le
Keyword(s):  
Optimality Conditions ◽  
Equilibrium Constraints ◽  
Dual Problems ◽  
Duality Relations ◽  
Infinite Programming ◽  
Convexity Assumptions ◽  
Necessary And Sufficient

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.

scholarly journals Nondifferentiable Minimax Programming Problems in Complex Spaces Involving Generalized Convex Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Anurag Jayswal ◽  
Ashish Kumar Prasad ◽  
Krishna Kummari
Keyword(s):  
Generalized Convexity ◽  
Sufficient Optimality Conditions ◽  
Generalized Convex Functions ◽  
Complex Spaces ◽  
Minimax Programming ◽  
Complex Functions ◽  
Primal And Dual Problems ◽  
Primal And Dual ◽  
Convexity Assumptions ◽  
Dual Models

We start our discussion with a class of nondifferentiable minimax programming problems in complex space and establish sufficient optimality conditions under generalized convexity assumptions. Furthermore, we derive weak, strong, and strict converse duality theorems for the two types of dual models in order to prove that the primal and dual problems will have no duality gap under the framework of generalized convexity for complex functions.

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.

scholarly journals New optimality conditions in vector continuous-time programming

2020 ◽  
pp. 28-28
Author(s):  
Aleksandar Jovic
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Continuous Time ◽  
Inequality Constraints ◽  
Sufficient Optimality Conditions ◽  
Generalized Concavity ◽  
Necessary And Sufficient

In this work vector continuous-time programming problem with inequality constraints is considered. The necessary and sufficient optimality conditions under generalized concavity assumptions are established. The results were formulated using differentiability.

scholarly journals Nondifferentiable generalized minimax fractional programming under (Ф,ρ)-invexity

2021 ◽  
pp. 18-18
Author(s):  
B.B. Upadhyay ◽  
T. Antczak ◽  
S.K. Mishra ◽  
K. Shukla
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Fractional Programming ◽  
Sufficient Optimality Conditions ◽  
Duality Theorems ◽  
Dual Problems ◽  
Fractional Programming Problem ◽  
Minimax Fractional Programming ◽  
Dual Models

In this paper, a class of nonconvex nondifferentiable generalized minimax fractional programming problems is considered. Sufficient optimality conditions for the considered nondifferentiable generalized minimax fractional programming problem are established under the concept of (?,?)-invexity. Further, two types of dual models are formulated and various duality theorems relating to the primal minimax fractional programming problem and dual problems are established. The results established in the paper generalize and extend several known results in the literature to a wider class of nondifferentiable minimax fractional programming problems. To the best of our knowledge, these results have not been established till now.

scholarly journals Invex optimisation problems

1992 ◽  
Vol 46 (1) ◽  
pp. 47-66 ◽  
Author(s):  
D.T. Luc ◽  
C. Malivert
Keyword(s):  
Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Dual Problems ◽  
Invex Set ◽  
Duality Property ◽  
Wolfe Type Dual ◽  
Necessary And Sufficient

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.

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.

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