scholarly journals Duality for multiobjective variational control and multiobjective fractional variational control problems with pseudoinvexity

2006 ◽  
Vol 2006 ◽  
pp. 1-15 ◽  
Author(s):  
C. Nahak
Keyword(s):  
Control Problems ◽  
Duality Theorems ◽  
Converse Duality ◽  
Duality Results

A class of multiobjective variational control and multiobjective fractional variational control problems is considered, and the duality results are formulated. Under pseudoinvexity assumptions on the functions involved, weak, strong, and converse duality theorems are proved.

scholarly journals On a Dual Pair of Multiobjective Interval-Valued Variational Control Problems

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 893
Author(s):  
Savin Treanţă
Keyword(s):  
Optimization Problems ◽  
Dual Pair ◽  
Control Problems ◽  
Integral Functionals ◽  
Duality Theorems ◽  
Converse Duality ◽  
New Class ◽  
Duality Results ◽  
Curvilinear Integral ◽  
Interval Valued

In this paper, by using the new concept of (ϱ,ψ,ω)-quasiinvexity associated with interval-valued path-independent curvilinear integral functionals, we establish some duality results for a new class of multiobjective variational control problems with interval-valued components. More concretely, we formulate and prove weak, strong, and converse duality theorems under (ϱ,ψ,ω)-quasiinvexity hypotheses for the considered class of optimization problems.

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 Higher-Order Generalized Invexity in Control Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
S. K. Padhan ◽  
C. Nahak
Keyword(s):  
Control Problem ◽  
Strong Duality ◽  
Higher Order ◽  
Control Problems ◽  
Weak Duality ◽  
Converse Duality ◽  
Generalized Invexity ◽  
Duality Results ◽  
Higher Order Duality

We introduce a higher-order duality (Mangasarian type and Mond-Weir type) for the control problem. Under the higher-order generalized invexity assumptions on the functions that compose the primal problems, higher-order duality results (weak duality, strong duality, and converse duality) are derived for these pair of problems. Also, we establish few examples in support of our investigation.

scholarly journals Generalised convexity and duality in multiple objective programming

1989 ◽  
Vol 39 (2) ◽  
pp. 287-299 ◽  
Author(s):  
T. Weir ◽  
B. Mond
Keyword(s):  
Multiple Objective Programming ◽  
Multiple Objective ◽  
Duality Theorems ◽  
Converse Duality ◽  
Duality Results ◽  
Objective Programming ◽  
Weak Minima ◽  
Convexity Conditions

By considering the concept of weak minima, different scalar duality results are extended to multiple objective programming problems. A number of weak, strong and converse duality theorems are given under a variety of generalised convexity conditions.

scholarly journals Duality Results in Quasiinvex Variational Control Problems with Curvilinear Integral Functionals

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 811 ◽  
Author(s):  
Cipu
Keyword(s):  
Control Problems ◽  
Integral Functionals ◽  
Converse Duality ◽  
Duality Results ◽  
Curvilinear Integral

In this paper, we formulate and prove weak, strong and converse duality results invariational control problems involving (ρ,b)-quasiinvex path-independent curvilinear integralcost functionals.

scholarly journals Nondifferentiable G-Mond–Weir Type Multiobjective Symmetric Fractional Problem and Their Duality Theorems under Generalized Assumptions

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1348 ◽  
Author(s):  
Ramu Dubey ◽  
Lakshmi Narayan Mishra ◽  
Luis Manuel Sánchez Ruiz
Keyword(s):  
Vector Optimization ◽  
Optimization Problem ◽  
Vector Optimization Problem ◽  
Second Order ◽  
Type Model ◽  
Dual Model ◽  
Duality Theorems ◽  
Converse Duality ◽  
Numerical Example ◽  
Primal Dual

In this article, a pair of nondifferentiable second-order symmetric fractional primal-dual model (G-Mond–Weir type model) in vector optimization problem is formulated over arbitrary cones. In addition, we construct a nontrivial numerical example, which helps to understand the existence of such type of functions. Finally, we prove weak, strong and converse duality theorems under aforesaid assumptions.

scholarly journals Mixed-type duality for multiobjective fractional variational control problems

2005 ◽  
Vol 2005 (1) ◽  
pp. 109-124 ◽  
Author(s):  
Raman Patel
Keyword(s):  
Nonlinear Programming ◽  
Convex Functions ◽  
Mixed Type ◽  
Efficient Solutions ◽  
Control Problems ◽  
Duality Results ◽  
Finite Dimensional ◽  
Duality Relations ◽  
Mixed Type Duality ◽  
Convexity Assumptions

The concept of mixed-type duality has been extended to the class of multiobjective fractional variational control problems. A number of duality relations are proved to relate the efficient solutions of the primal and its mixed-type dual problems. The results are obtained forρ-convex (generalizedρ-convex) functions. The results generalize a number of duality results previously obtained for finite-dimensional nonlinear programming problems under various convexity assumptions.

scholarly journals On Nonsmooth Semi-Infinite Minimax Programming Problem with(Φ,ρ)-Invexity

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
X. L. Liu ◽  
G. M. Lai ◽  
C. Q. Xu ◽  
D. H. Yuan
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Necessary Optimality Conditions ◽  
Duality Theorems ◽  
Converse Duality ◽  
Minimax Programming ◽  
Carathéodory’S Theorem

We are interested in a nonsmooth minimax programming Problem (SIP). Firstly, we establish the necessary optimality conditions theorems for Problem (SIP) when using the well-known Caratheodory's theorem. Under the Lipschitz(Φ,ρ)-invexity assumptions, we derive the sufficiency of the necessary optimality conditions for the same problem. We also formulate dual and establish weak, strong, and strict converse duality theorems for Problem (SIP) and its dual. These results extend several known results to a wider class of problems.

scholarly journals Multiobjective duality with ρ−(η,θ)-invexity

2005 ◽  
Vol 2005 (2) ◽  
pp. 175-180 ◽  
Author(s):  
C. Nahak ◽  
S. Nanda
Keyword(s):  
Programming Problem ◽  
Multiobjective Programming ◽  
Efficient Solutions ◽  
Duality Theorems ◽  
Converse Duality ◽  
Dual Problems ◽  
Properly Efficient Solutions ◽  
Multiobjective Programming Problem ◽  
Primal And Dual Problems ◽  
Primal And Dual

Under ρ−(η,θ)-invexity assumptions on the functions involved, weak, strong, and converse duality theorems are proved to relate properly efficient solutions of the primal and dual problems for a multiobjective programming problem.

scholarly journals Symmetric duality for Bonvex multiobjective fractional continuous time programming problems

2010 ◽  
Vol 7 (2) ◽  
pp. 413-424
Author(s):  
Deo Brat Ojha
Keyword(s):  
Continuous Time ◽  
Efficient Solutions ◽  
Weak Duality ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Converse Duality ◽  
Multi Objective ◽  
Properly Efficient Solutions ◽  
Self Duality ◽  
Duality Relations

We introduced a symmetric dual for multi objective fractional variational programs in second order. Under invexity assumptions, we established weak, strong and converse duality as well as self duality relations .We work with properly efficient solutions in strong and converse duality theorems. The weak duality theorems involves efficient solutions .

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