ON OPTIMALITY AND DUALITY IN INTERVAL-VALUED VARIATIONAL PROBLEM WITH B-(p,r)-INVEXITY

Duality Theorems ◽

Real World Problem ◽

Sufficiency Theorem ◽

Optimality And Duality ◽

Definition Of ◽

In this paper, we consider a class of interval-valued variational optimization problem. We extend the definition of B -( p,r )- invexity which was originally defined for scalar optimization problem to the interval-valued variational problem. The necessary and sufficient optimality conditions for the problem have been established under B -( p,r )-invexity assumptions. An application, showing utility of the sufficiency theorem in real-world problem, has also been provided. In addition to this, for an interval- optimization problem Mond-Weir and Wolfe type duals are presented and related duality theorems have been proved. Non-trivial examples verifying the results have also been presented throughout the paper.

Optimality and duality in set-valued optimization utilizing limit sets

Open Mathematics ◽

10.1515/math-2018-0095 ◽

2018 ◽

Vol 16 (1) ◽

pp. 1128-1139

Author(s):

Xiangyu Kong ◽

Yinfeng Zhang ◽

GuoLin Yu

Keyword(s):

Optimality Conditions ◽

Duality Theory ◽

Optimization Problem ◽

Convex Set ◽

Constraint Optimization ◽

Limit Sets ◽

Optimality And Duality ◽

Wolfe Type Dual ◽

AbstractThis paper deals with optimality conditions and duality theory for vector optimization involving non-convex set-valued maps. Firstly, under the assumption of nearly cone-subconvexlike property for set-valued maps, the necessary and sufficient optimality conditions in terms of limit sets are derived for local weak minimizers of a set-valued constraint optimization problem. Then, applications to Mond-Weir type and Wolfe type dual problems are presented.

An International Journal of Optimization and Control Theories & Applications (IJOCTA) ◽

Vector optimization with cone semilocally preinvex functions

10.11121/ijocta.01.2014.00162 ◽

2013 ◽

Vol 4 (1) ◽

pp. 11-20 ◽

Cited By ~ 1

Author(s):

Surjeet Kaur Suneja ◽

Meetu Bhatia

Keyword(s):

Optimality Conditions ◽

Vector Optimization ◽

Minimization Problem ◽

Optimization Problem ◽

Vector Optimization Problem ◽

Duality Theorems ◽

Preinvex Functions ◽

In this paper we introduce cone semilocally preinvex, cone semilocally quasi preinvex and cone semilocally pseudo preinvex functions and study their properties. These functions are further used to establish necessary and sufficient optimality conditions for a vector minimization problem over cones. A Mond-Weir type dual is formulated for the vector optimization problem and various duality theorems are proved.

Necessary and sufficient optimality conditions for non-linear unconstrained and constrained optimization problem with interval valued objective function

Computers & Industrial Engineering ◽

10.1016/j.cie.2020.106634 ◽

2020 ◽

Vol 147 ◽

pp. 106634

Author(s):

Md Sadikur Rahman ◽

Ali Akbar Shaikh ◽

Asoke Kumar Bhunia

Keyword(s):

Constrained Optimization ◽

Objective Function ◽

Optimality Conditions ◽

Optimization Problem ◽

Constrained Optimization Problem ◽

Non Linear ◽

Robust Approximate Optimality Conditions for Uncertain Nonsmooth Optimization with Infinite Number of Constraints

Mathematics ◽

10.3390/math7010012 ◽

2018 ◽

Vol 7 (1) ◽

pp. 12 ◽

Cited By ~ 7

Author(s):

Xiangkai Sun ◽

Hongyong Fu ◽

Jing Zeng

Keyword(s):

Optimality Conditions ◽

Optimization Problem ◽

Constraint Qualification ◽

Optimization Problems ◽

Optimization Technique ◽

Optimal Solution ◽

Convex Constraint ◽

Approximate Optimality Conditions ◽

This paper deals with robust quasi approximate optimal solutions for a nonsmooth semi-infinite optimization problems with uncertainty data. By virtue of the epigraphs of the conjugates of the constraint functions, we first introduce a robust type closed convex constraint qualification. Then, by using the robust type closed convex constraint qualification and robust optimization technique, we obtain some necessary and sufficient optimality conditions for robust quasi approximate optimal solution and exact optimal solution of this nonsmooth uncertain semi-infinite optimization problem. Moreover, the obtained results in this paper are applied to a nonsmooth uncertain optimization problem with cone constraints.

Optimality and duality for nonsmooth semi-infinite E-convex multi-objective programming with support functions

International Journal for Simulation and Multidisciplinary Design Optimization ◽

10.1051/smdo/2020011 ◽

2020 ◽

Vol 11 ◽

pp. 17

Author(s):

Tarek Emam

Keyword(s):

Strong Duality ◽

Convex Programming Problem ◽

Duality Theorems ◽

Support Functions ◽

Primal Problem ◽

Multi Objective ◽

Multi Objective Programming ◽

Optimality And Duality ◽

Convexity Assumptions

In this paper, we study a nonsmooth semi-infinite multi-objective E-convex programming problem involving support functions. We derive sufficient optimality conditions for the primal problem. We formulate Mond-Weir type dual for the primal problem and establish weak and strong duality theorems under various generalized E-convexity assumptions.

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

The Scientific World JOURNAL ◽

10.1155/2014/750910 ◽

2014 ◽

Vol 2014 ◽

pp. 1-5 ◽

Cited By ~ 5

Author(s):

Vasile Preda

Keyword(s):

Optimization Problems ◽

Directional Derivative ◽

Efficient Solutions ◽

Dini Derivative ◽

Duality Results ◽

Multiobjective Problem ◽

Generalized Convexities ◽

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.

Optimality conditions for nonsmooth interval-valued and multiobjective semi-infinite programming

RAIRO - Operations Research ◽

10.1051/ro/2020066 ◽

2020 ◽

Author(s):

Mohsine Jennane ◽

El Mostafa Kalmoun ◽

Lahoussine Lafhim

Keyword(s):

Optimality Conditions ◽

Optimization Problem ◽

Constraint Qualification ◽

Necessary Optimality Conditions ◽

Convexity Assumption ◽

Locally Lipschitz ◽

Infinite Programming ◽

Asymptotic Convexity ◽

We consider a nonsmooth semi-infinite interval-valued vector programming problem, where the objectives and constraints functions need not to be locally Lipschitz. Using Abadie's constraint qualification and convexificators, we provide Karush-Kuhn-Tucker necessary optimality conditions by converting the initial problem into a bi-criteria optimization problem. Furthermore, we establish sufficient optimality conditions under the asymptotic convexity assumption.

Optimality and duality for a class of nondifferentiable minimax fractional programming problems

Yugoslav journal of operations research ◽

10.2298/yjor0901049b ◽

2009 ◽

Vol 19 (1) ◽

pp. 49-61

Author(s):

Antoan Bătătorescu ◽

Miruna Beldiman ◽

Iulian Antonescu ◽

Roxana Ciumara

Keyword(s):

Optimality Conditions ◽

Fractional Programming ◽

Dual Problem ◽

Square Root ◽

Duality Results ◽

Minimax Fractional Programming ◽

Optimality And Duality ◽

Necessary and sufficient optimality conditions are established for a class of nondifferentiable minimax fractional programming problems with square root terms. Subsequently, we apply the optimality conditions to formulate a parametric dual problem and we prove some duality results.

Optimality and Duality with Respect to b-(E,m)-Convex Programming

Symmetry ◽

10.3390/sym10120774 ◽

2018 ◽

Vol 10 (12) ◽

pp. 774

Author(s):

Bo Yu ◽

Jiagen Liao ◽

Tingsong Du

Keyword(s):

Convex Programming ◽

Convex Sets ◽

Sufficient Conditions ◽

Optimality Criteria ◽

Duality Theorems ◽

Symmetric Duality ◽

Convex Mappings ◽

Uniqueness Of The Solution ◽

Optimality And Duality

Noticing that E -convexity, m-convexity and b-invexity have similar structures in their definitions, there are some possibilities to treat these three class of mappings uniformly. For this purpose, the definitions of the ( E , m ) -convex sets and the b- ( E , m ) -convex mappings are introduced. The properties concerning operations that preserve the ( E , m ) -convexity of the proposed mappings are derived. The unconstrained and inequality constrained b- ( E , m ) -convex programming are considered, where the sufficient conditions of optimality are developed and the uniqueness of the solution to the b- ( E , m ) -convex programming are investigated. Furthermore, the sufficient optimality conditions and the Fritz–John necessary optimality criteria for nonlinear multi-objective b- ( E , m ) -convex programming are established. The Wolfe-type symmetric duality theorems under the b- ( E , m ) -convexity, including weak and strong symmetric duality theorems, are also presented. Finally, we construct two examples in detail to show how the obtained results can be used in b- ( E , m ) -convex programming.

An International Journal of Optimization and Control Theories & Applications (IJOCTA) ◽

On G-invexity-type nonlinear programming problems

10.11121/ijocta.01.2015.00202 ◽

2015 ◽

Vol 5 (1) ◽

pp. 13-20

Author(s):

Tadeusz Antczak ◽

Keyword(s):

Optimization Problem ◽

Dual Problem ◽

Optimization Problems ◽

Sufficient Conditions ◽

Inequality Constraints ◽

Extremum Problem ◽

New Class ◽

Wolfe Dual

In this paper, we introduce the concepts of KT-G-invexity and WD$-G-invexity for the considered differentiable optimization problem with inequality constraints. Using KT-G-invexity notion, we prove new necessary and sufficient optimality conditions for a new class of such nonconvex differentiable optimization problems. Further, the so-called G-Wolfe dual problem is defined for the considered extremum problem with inequality constraints. Under WD-G-invexity assumption, the necessary and sufficient conditions for weak duality between the primal optimization problem and its G-Wolfe dual problem are also established.