scholarly journals gH-Symmetrically Derivative of Interval-Valued Functions and Applications in Interval-Valued Optimization

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1203
Author(s):  
Guo ◽  
Ye ◽  
Zhao ◽  
Liu
Keyword(s):  
Optimization Problems ◽  
Kkt Conditions ◽  
Symmetrical Derivative ◽  
Interval Valued

In this paper, we present the gH-symmetrical derivative of interval-valued functions andits properties. In application, we apply this new derivative to investigate the Karush–Kuhn–Tucker(KKT) conditions of interval-valued optimization problems. Meanwhile, some examples are workedout to illuminate the obtained results.

Optimization of the mathematical programming and applications

2021 ◽  
Vol 2 (5) ◽  
pp. 7902-7911
Author(s):  
Johnny Moisés Valverde Montoro ◽  
Milton Milciades Cortez Gutiérrez ◽  
Hernán Oscar Cortez Gutiérrez
Keyword(s):  
Mathematical Programming ◽  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Optimization Problems ◽  
Kkt Conditions ◽  
Objective Functions ◽  
Multiobjective Optimization Problems ◽  
Interval Valued

The present investigation responds to the need to solve optimization problems with optimality conditions. The KKT conditions are considered for multiobjective optimization problems with interval-valued objective functions.

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.

scholarly journals On interval-valued invex mappings and optimality conditions for interval-valued optimization problems

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Lifeng Li ◽  
Sanyang Liu ◽  
Jianke Zhang
Keyword(s):  
Optimality Conditions ◽  
Optimization Problems ◽  
Interval Valued

scholarly journals Interval-Valued Optimization Problems Involvingα,ρ-Right Upper-Dini-Derivative Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Vasile Preda
Keyword(s):  
Optimization Problems ◽  
Directional Derivative ◽  
Efficient Solutions ◽  
Sufficient Optimality Conditions ◽  
Dini Derivative ◽  
Duality Results ◽  
Multiobjective Problem ◽  
Necessary And Sufficient ◽  
Generalized Convexities ◽  
Interval Valued

We consider an interval-valued multiobjective problem. Some necessary and sufficient optimality conditions for weak efficient solutions are established under new generalized convexities with the tool-right upper-Dini-derivative, which is an extension of directional derivative. Also some duality results are proved for Wolfe and Mond-Weir duals.

scholarly journals Some Inequalities Related to Interval-Valued η h -Convex Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Lei Chen ◽  
Muhammad Shoaib Saleem ◽  
Muhammad Sajid Zahoor ◽  
Rahat Bano
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Optimization Problems ◽  
Extended Version ◽  
Interval Valued

Convexity plays an important role in many areas of mathematics, especially in the study of optimization problems where they are distinguished by a number of convenient properties. Our aim is to introduce a more extended version of convexity. In this paper, we introduced interval-valued generalized η h convex function and proved Hermite–Hadamard-, Jensen-, and Ostrowski-type inequalities in this generalization. The presented results are generalizations of many existing results of literature.

scholarly journals Some new Jensen, Schur and Hermite-Hadamard inequalities for log convex fuzzy interval-valued functions

2021 ◽  
Vol 7 (3) ◽  
pp. 4338-4358
Author(s):  
Muhammad Bilal Khan ◽  
◽  
Hari Mohan Srivastava ◽  
Pshtiwan Othman Mohammed ◽  
Kamsing Nonlaopon ◽  
...  
Keyword(s):  
Convex Functions ◽  
Optimization Problems ◽  
Fuzzy Optimization ◽  
Order Relation ◽  
Inclusion Relation ◽  
Nonconvex Functions ◽  
New Directions ◽  
Fuzzy Order ◽  
Interval Valued ◽  
Fuzzy Interval

<abstract> <p>The inclusion relation and the order relation are two distinct ideas in interval analysis. Convexity and nonconvexity create a significant link with different sorts of inequalities under the inclusion relation. For many classes of convex and nonconvex functions, many works have been devoted to constructing and refining classical inequalities. However, it is generally known that log-convex functions play a significant role in convex theory since they allow us to deduce more precise inequalities than convex functions. Because the idea of log convexity is so important, we used fuzzy order relation $\left(\preceq \right)$ to establish various discrete Jensen and Schur, and Hermite-Hadamard (H-H) integral inequality for log convex fuzzy interval-valued functions (L-convex F-I-V-Fs). Some nontrivial instances are also offered to bolster our findings. Furthermore, we show that our conclusions include as special instances some of the well-known inequalities for L-convex F-I-V-Fs and their variant forms. Furthermore, we show that our conclusions include as special instances some of the well-known inequalities for L-convex F-I-V-Fs and their variant forms. These results and different approaches may open new directions for fuzzy optimization problems, modeling, and interval-valued functions.</p> </abstract>

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