scholarly journals Optimality conditions for invex interval valued nonlinear programming problems involving generalized H-derivative

Filomat ◽  
2016 ◽  
Vol 30 (8) ◽  
pp. 2121-2138 ◽  
Author(s):  
Izhar Ahmad ◽  
Deepak Singh ◽  
Bilal Dar
Keyword(s):  
Nonlinear Programming ◽  
Optimality Conditions ◽  
Generalized Convexity ◽  
Optimal Solutions ◽  
Solution Concepts ◽  
Lagrangian Multipliers ◽  
Kkt Optimality Conditions ◽  
Generalized Hukuhara Differentiability ◽  
Interval Valued

In this paper, some interval valued programming problems are discussed. The solution concepts are adopted from Wu [7] and Chalco-Cano et al. [34]. By considering generalized Hukuhara differentiability and generalized convexity (viz. ?-preinvexity, ?-invexity etc.) of interval valued functions, the KKT optimality conditions for obtaining (LS and LU) optimal solutions are elicited by introducing Lagrangian multipliers. Our results generalize the results of Wu [7], Zhang et al. [11] and Chalco-Cano et al. [34]. To illustrate our theorems suitable examples are also provided

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.

scholarly journals The Karush-Kuhn-Tucker Optimality Conditions for the Fuzzy Optimization Problems in the Quotient Space of Fuzzy Numbers

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Nanxiang Yu ◽  
Dong Qiu
Keyword(s):  
Optimality Conditions ◽  
Fuzzy Numbers ◽  
Quotient Space ◽  
Optimization Problems ◽  
Lagrange Function ◽  
Fuzzy Optimization ◽  
Solution Concepts ◽  
Kkt Optimality Conditions

We propose the solution concepts for the fuzzy optimization problems in the quotient space of fuzzy numbers. The Karush-Kuhn-Tucker (KKT) optimality conditions are elicited naturally by introducing the Lagrange function multipliers. The effectiveness is illustrated by examples.

scholarly journals On Modified Interval-Valued Variational Control Problems with First-Order PDE Constraints

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 472
Author(s):  
Savin Treanţă
Keyword(s):  
Partial Differential Equations ◽  
Control Problem ◽  
Optimality Conditions ◽  
Generalized Convexity ◽  
Inequality Constraints ◽  
Control Problems ◽  
First Order ◽  
First Order Pde ◽  
Convexity Assumptions ◽  
Interval Valued

In this paper, a modified interval-valued variational control problem involving first-order partial differential equations (PDEs) and inequality constraints is investigated. Specifically, under some generalized convexity assumptions, we formulate and prove LU-optimality conditions for the considered interval-valued variational control problem. In order to illustrate the main results and their effectiveness, an application is provided.

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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