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

2020 ◽  
Vol 11 ◽  
pp. 17
Author(s):  
Tarek Emam
Keyword(s):  
Strong Duality ◽  
Sufficient Optimality Conditions ◽  
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.

scholarly journals Optimality and duality for nonsmooth semi-infinite multiobjective programming with support functions

2017 ◽  
Vol 27 (2) ◽  
pp. 205-218 ◽  
Author(s):  
Yadvendra Singh ◽  
S.K. Mishra ◽  
K.K. Lai
Keyword(s):  
Generalized Convexity ◽  
Multiobjective Programming ◽  
Sufficient Optimality Conditions ◽  
Duality Theorems ◽  
Support Functions ◽  
Primal Problem ◽  
Special Cases ◽  
Multiobjective Programming Problem ◽  
Optimality And Duality ◽  
Convexity Assumptions

In this paper, we consider a nonsmooth semi-infinite multiobjective programming problem involving support functions. We establish sufficient optimality conditions for the primal problem. We formulate Mond-Weir type dual for the primal problem and establish weak, strong and strict converse duality theorems under various generalized convexity assumptions. Moreover, some special cases of our problem and results are presented.

scholarly journals On generalised convex mathematical programming

1992 ◽  
Vol 34 (1) ◽  
pp. 43-53 ◽  
Author(s):  
V. Jeyakumar ◽  
B. Mond
Keyword(s):  
Scalar Case ◽  
Sufficient Optimality Conditions ◽  
Convex Programming Problem ◽  
Multi Objective ◽  
New Class ◽  
Duality Results ◽  
Special Cases ◽  
Nonlinear Composite ◽  
Optimality And Duality ◽  
Image Position

AbstractThe sufficient optimality conditions and duality results have recently been given for the following generalised convex programming problem:where the funtion f and g satisfyfor some η: X0 × X0 → ℝnIt is shown here that a relaxation defining the above generalised convexity leads to a new class of multi-objective problems which preserves the sufficient optimality and duality results in the scalar case, and avoids the major difficulty of verifying that the inequality holds for the same function η(. , .). Further, this relaxation allows one to treat certain nonlinear multi-objective fractional programming problems and some other classes of nonlinear (composite) problems as special cases.

scholarly journals Optimality and duality for complex multi-objective programming

2022 ◽  
Vol 12 (1) ◽  
pp. 121
Author(s):  
Tone-Yau Huang ◽  
Tamaki Tanaka
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Efficient Solutions ◽  
Dual Model ◽  
Duality Theorems ◽  
Multi Objective ◽  
Multi Objective Programming ◽  
Optimality And Duality ◽  
Objective Programming

<p style='text-indent:20px;'>We consider a complex multi-objective programming problem (CMP). In order to establish the optimality conditions of problem (CMP), we introduce several properties of optimal efficient solutions and scalarization techniques. Furthermore, a certain parametric dual model is discussed, and their duality theorems are proved.</p>

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

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 774
Author(s):  
Bo Yu ◽  
Jiagen Liao ◽  
Tingsong Du
Keyword(s):  
Convex Programming ◽  
Convex Sets ◽  
Sufficient Conditions ◽  
Optimality Criteria ◽  
Sufficient Optimality Conditions ◽  
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.

On the multiobjective control problem

2018 ◽  
Vol 24 (2) ◽  
pp. 223-231
Author(s):  
Promila Kumar ◽  
Bharti Sharma
Keyword(s):  
Control Problem ◽  
Strong Duality ◽  
Efficient Solutions ◽  
Higher Order ◽  
Sufficient Optimality Conditions ◽  
Duality Theorems ◽  
Multiobjective Control ◽  
Primal And Dual Problems ◽  
Primal And Dual

Abstract In this paper, sufficient optimality conditions are established for the multiobjective control problem using efficiency of higher order as a criterion for optimality. The ρ-type 1 invex functionals (taken in pair) of higher order are proposed for the continuous case. Existence of such functionals is confirmed by a number of examples. It is shown with the help of an example that this class is more general than the existing class of functionals. Weak and strong duality theorems are also derived for a mixed dual in order to relate efficient solutions of higher order for primal and dual problems.

scholarly journals Duality for a class of second order symmetric nondifferentiable fractional variational problems

2020 ◽  
Vol 30 (2) ◽  
pp. 121-136
Author(s):  
Ashish Prasad ◽  
Anant Singh ◽  
Sony Khatri
Keyword(s):  
Variational Problems ◽  
Second Order ◽  
Static Case ◽  
Time Dependency ◽  
Duality Theorems ◽  
Support Functions ◽  
Converse Duality ◽  
Cone Constraints ◽  
Fractional Variational Problems ◽  
Convexity Assumptions

The present work frames a pair of symmetric dual problems for second order nondifferentiable fractional variational problems over cone constraints with the help of support functions. Weak, strong and converse duality theorems are derived under second order F-convexity assumptions. By removing time dependency, static case of the problem is obtained. Suitable numerical example is constructed.

scholarly journals Minimax fractional programming involving generalised invex functions

2003 ◽  
Vol 44 (3) ◽  
pp. 339-354 ◽  
Author(s):  
H. C. Lai ◽  
J. C. Liu
Keyword(s):  
Fractional Programming ◽  
Sufficient Optimality Conditions ◽  
Duality Theorems ◽  
Existence Of A Solution ◽  
Invex Functions ◽  
Minimax Fractional Programming ◽  
Convexity Assumptions ◽  
Wolfe Type Dual ◽  
Dual Models ◽  
Variational Type

AbstractThe convexity assumptions for a minimax fractional programming problem of variational type are relaxed to those of a generalised invexity situation. Sufficient optimality conditions are established under some specific assumptions. Employing the existence of a solution for the minimax variational fractional problem, three dual models, the Wolfe type dual, the Mond-Weir type dual and a one parameter dual type, are constructed. Several duality theorems concerning weak, strong and strict converse duality under the framework of invexity are proved.

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