scholarly journals Optimality Conditions and Duality for a Class of Generalized Convex Interval-Valued Optimization Problems

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2979
Author(s):  
Yating Guo ◽  
Guoju Ye ◽  
Wei Liu ◽  
Dafang Zhao ◽  
Savin Treanţǎ
Keyword(s):  
Optimality Conditions ◽  
Optimization Problems ◽  
Duality Theorems ◽  
Interval Valued ◽  
Quasi Convexity

This paper is devoted to derive optimality conditions and duality theorems for interval-valued optimization problems based on gH-symmetrically derivative. Further, the concepts of symmetric pseudo-convexity and symmetric quasi-convexity for interval-valued functions are proposed to extend above optimization conditions. Examples are also presented to illustrate corresponding results.

scholarly journals Duality Theorems for (ρ,ψ,d)-Quasiinvex Multiobjective Optimization Problems with Interval-Valued Components

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 894
Author(s):  
Savin Treanţă
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Integral Functional ◽  
Multiple Integral ◽  
Control Problems ◽  
Duality Theorems ◽  
New Class ◽  
Duality Results ◽  
Multiobjective Optimization Problems ◽  
Interval Valued

The present paper deals with a duality study associated with a new class of multiobjective optimization problems that include the interval-valued components of the ratio vector. More precisely, by using the new notion of (ρ,ψ,d)-quasiinvexity associated with an interval-valued multiple-integral functional, we formulate and prove weak, strong, and converse duality results for the considered class of variational control problems.

The Karush–Kuhn–Tucker conditions for multiple objective fractional interval valued optimization problems

2020 ◽  
Vol 54 (4) ◽  
pp. 1161-1188
Author(s):  
Indira P. Debnath ◽  
Shiv K. Gupta
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Pareto Optimality ◽  
Optimization Problems ◽  
Solution Concept ◽  
Multiple Objective ◽  
Clear Understanding ◽  
Interval Valued

In this article, we focus on a class of a fractional interval multivalued programming problem. For the solution concept, LU-Pareto optimality and LS-Pareto, optimality are discussed, and some nontrivial concepts are also illustrated with small examples. The ideas of LU-V-invex and LS-V-invex for a fractional interval problem are introduced. Using these invexity suppositions, we establish the Karush–Kuhn–Tucker optimality conditions for the problem assuming the functions involved to be gH-differentiable. Non-trivial examples are discussed throughout the manuscript to make a clear understanding of the results established. Results obtained in this paper unify and extend some previously known results appeared in the literature.

scholarly journals Karush-Kuhn-Tucker optimality conditions for a class of robust optimization problems with an interval-valued objective function

2020 ◽  
Vol 18 (1) ◽  
pp. 781-793
Author(s):  
Jing Zhao ◽  
Maojun Bin
Keyword(s):  
Banach Space ◽  
Robust Optimization ◽  
Objective Function ◽  
Optimality Conditions ◽  
Optimization Problems ◽  
Data Uncertainty ◽  
Nondominated Solutions ◽  
The Face ◽  
Interval Valued

Abstract In this article, we study the nonlinear and nonsmooth interval-valued optimization problems in the face of data uncertainty, which are called interval-valued robust optimization problems (IVROPs). We introduce the concept of nondominated solutions for the IVROP. If the interval-valued objective function f and constraint functions {g}_{i} are nonsmooth on Banach space E, we establish a nonsmooth and robust Karush-Kuhn-Tucker optimality theorem.

scholarly journals A Theoretical Framework for Optimality Conditions of Nonlinear Type-2 Interval-Valued Unconstrained and Constrained Optimization Problems Using Type-2 Interval Order Relations

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 908
Author(s):  
Md Sadikur Rahman ◽  
Ali Akbar Shaikh ◽  
Irfan Ali ◽  
Asoke Kumar Bhunia ◽  
Armin Fügenschuh
Keyword(s):  
Constrained Optimization ◽  
Optimality Conditions ◽  
Nonlinear Optimization ◽  
Optimization Problems ◽  
Interval Order ◽  
Constrained Optimization Problems ◽  
Interval Approach ◽  
Kkt Optimality Conditions ◽  
Interval Valued

In the traditional nonlinear optimization theory, the Karush-Kuhn-Tucker (KKT) optimality conditions for constrained optimization problems with inequality constraints play an essential role. The situation becomes challenging when the theory of traditional optimization is discussed under uncertainty. Several researchers have discussed the interval approach to tackle nonlinear optimization uncertainty and derived the optimality conditions. However, there are several realistic situations in which the interval approach is not suitable. This study aims to introduce the Type-2 interval approach to overcome the limitation of the classical interval approach. This study introduces Type-2 interval order relation and Type-2 interval-valued function concepts to derive generalized KKT optimality conditions for constrained optimization problems under uncertain environments. Then, the optimality conditions are discussed for the unconstrained Type-2 interval-valued optimization problem and after that, using these conditions, generalized KKT conditions are derived. Finally, the proposed approach is demonstrated by numerical examples.

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