scholarly journals On Constrained Set-Valued Semi-Infinite Programming Problems with ρ-Cone Arcwise Connectedness

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 302
Author(s):  
Koushik Das ◽  
Savin Treanţă
Keyword(s):  
Programming Problem ◽  
Kkt Conditions ◽  
Duality Results ◽  
Contingent Epiderivative ◽  
Arcwise Connectedness ◽  
Infinite Programming

In this paper, we establish sufficient Karush–Kuhn–Tucker (for short, KKT) conditions of a set-valued semi-infinite programming problem (SP) via the notion of contingent epiderivative of set-valued maps. We also derive duality results of Mond–Weir (MWD), Wolfe (WD), and mixed (MD) types of the problem (SP) under ρ-cone arcwise connectedness assumptions.

scholarly journals Sufficiency and duality of set-valued fractional programming problems via second-order contingent epiderivative

2021 ◽  
pp. 19-19
Author(s):  
Koushik Das
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Fractional Programming ◽  
Second Order ◽  
Primal Problem ◽  
Duality Results ◽  
Contingent Epiderivative ◽  
Convexity Assumptions ◽  
Mixed Types ◽  
Cone Convexity

In this paper, we establish second-order sufficient KKT optimality conditions of a set-valued fractional programming problem under second-order generalized cone convexity assumptions. We also prove duality results between the primal problem and second-order dual problems of parametric, Mond-Weir, Wolfe, and mixed types via the notion of second-order contingent epiderivative.

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 Generalized(ℱ,b,ϕ,ρ,θ)-univexn-set functions and parametric duality models in minmax fractional subset programming

2005 ◽  
Vol 2005 (10) ◽  
pp. 1601-1620 ◽  
Author(s):  
G. J. Zalmai
Keyword(s):  
Programming Problem ◽  
Duality Results ◽  
Set Functions

We construct three parametric duality models and establish a fairly large number of duality results under a variety of generalized(ℱ,b,ϕ,ρ,θ)-univexity assumptions for a discrete minmax fractional subset programming problem.

Nonsmooth semi-infinite programming problem using Limiting subdifferentials

2011 ◽  
Vol 53 (2) ◽  
pp. 285-296 ◽  
Author(s):  
S. K. Mishra ◽  
M. Jaiswal ◽  
H. A. Le Thi
Keyword(s):  
Programming Problem ◽  
Infinite Programming

scholarly journals On approximate solutions for convex semi-infinite programming with uncertainty

2020 ◽  
Author(s):  
Ke Su ◽  
Yumeng Lin ◽  
Chen Wang
Keyword(s):  
Approximate Solution ◽  
Constraint Qualification ◽  
Optimization Problems ◽  
Approximate Solutions ◽  
Necessary Condition ◽  
Optimization Approach ◽  
Duality Results ◽  
Cone Constraint ◽  
Lagrangian Dual ◽  
Infinite Programming

In this paper, we consider approximate solutions (also called $\varepsilon$-solutions) for semi-infinite optimization problems that objective function and constraint functions with uncertainty data are all convex, and establish robust counterpart of convex semi-infinite program and then consider approximate solutions for its. Moreover, the robust necessary condition and robust sufficient theorems are obtained. Then the duality results of the Lagrangian dual approximate solution is given by the robust optimization approach under a cone constraint qualification.

Duality relations for second-order programming problem under (G,αf)-bonvexity assumptions

2018 ◽  
Vol 13 (02) ◽  
pp. 2050044 ◽  
Author(s):  
Ramu Dubey ◽  
Vishnu Narayan Mishra ◽  
Puneet Tomar
Keyword(s):  
Programming Problem ◽  
Duality Theorem ◽  
Optimization Problem ◽  
Second Order ◽  
Dual Model ◽  
Weak Duality ◽  
Numerical Examples ◽  
Duality Results ◽  
Duality Relations ◽  
Definition Of

In this paper, we introduce the definition of [Formula: see text]-bonvex/[Formula: see text]-pseudobonvex functions and to show the existence of such functions, we construct nontrivial numerical examples. In the next section, we formulate a pair of second-order symmetric dual model in optimization problem and proved the duality results under [Formula: see text]-bonvexity/[Formula: see text]-pseudobonvexity assumptions. Further, we also construct nontrivial concrete examples which justifying definitions as well as the weak duality theorem presented in the paper.

Symmetric duality results for second-order nondifferentiable multiobjective programming problem

2019 ◽  
Vol 53 (2) ◽  
pp. 539-558 ◽  
Author(s):  
Ramu Dubey ◽  
Vishnu Narayan Mishra
Keyword(s):  
Programming Problem ◽  
Duality Theorem ◽  
Multiobjective Programming ◽  
Second Order ◽  
Weak Duality ◽  
Symmetric Duality ◽  
Numerical Examples ◽  
Duality Results ◽  
Duality Relations ◽  
Multiobjective Programming Problem

In this article, we study the existence of Gf-bonvex/Gf -pseudo-bonvex functions and construct various nontrivial numerical examples for the existence of such type of functions. Furthermore, we formulate Mond-Weir type second-order nondifferentiable multiobjective programming problem and give a nontrivial concrete example which justify weak duality theorem present in the paper. Next, we prove appropriate duality relations under aforesaid assumptions.

Sign in / Sign up

Export Citation Format

Share Document