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.

Higher order duality for cone vector optimization problems

2018 ◽  
Vol 13 (01) ◽  
pp. 2050020
Author(s):  
Vivek Singh ◽  
Anurag Jayswal ◽  
S. Al-Homidan ◽  
I. Ahmad
Keyword(s):  
Vector Optimization ◽  
Optimization Problems ◽  
Strong Duality ◽  
Vector Optimization Problem ◽  
Higher Order ◽  
Support Functions ◽  
Invex Functions ◽  
New Class ◽  
Duality Results ◽  
Higher Order Duality

In this paper, we present a new class of higher order [Formula: see text]-[Formula: see text]-invex functions over cones. Further, we formulate two types of higher order dual models for a vector optimization problem over cones containing support functions in objectives as well as in constraints and establish several duality results, viz., weak and strong duality results.

scholarly journals On geometric duality for state-constrained control problems

1979 ◽  
Vol 20 (2) ◽  
pp. 301-312
Author(s):  
T.R. Jefferson ◽  
C.H. Scott
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
State Constraints ◽  
Strong Duality ◽  
State Constraint ◽  
Continuous Functions ◽  
Control Problems ◽  
Absolutely Continuous Functions ◽  
Pure State Constraints ◽  
Constrained Control Problems

For convex optimal control problems without explicit pure state constraints, the structure of dual problems is now well known. However, when these constraints are present and active, the theory of duality is not highly developed. The major difficulty is that the dual variables are not absolutely continuous functions as a result of singularities when the state trajectory hits a state constraint. In this paper we recognize this difficulty by formulating the dual probram in the space of measurable functions. A strong duality theorem is derived. This pairs a primal, state constrained convex optimal control problem with a dual convex control problem that is unconstrained with respect to state constraints. In this sense, the dual problem is computationally more attractive than the primal.

scholarly journals A Kind of New Higher-Order Mond-Weir Type Duality for Set-Valued Optimization Problems

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 372
Author(s):  
Liu He ◽  
Qi-Lin Wang ◽  
Ching-Feng Wen ◽  
Xiao-Yan Zhang ◽  
Xiao-Bing Li
Keyword(s):  
Existence Theorem ◽  
Lower Order ◽  
Optimization Problem ◽  
Dual Problem ◽  
Optimization Problems ◽  
Strong Duality ◽  
Higher Order ◽  
Weak Duality ◽  
Duality Theorems ◽  
Benson Proper Efficiency

In this paper, we introduce the notion of higher-order weak adjacent epiderivative for a set-valued map without lower-order approximating directions and obtain existence theorem and some properties of the epiderivative. Then by virtue of the epiderivative and Benson proper efficiency, we establish the higher-order Mond-Weir type dual problem for a set-valued optimization problem and obtain the corresponding weak duality, strong duality and converse duality theorems, respectively.

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 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.

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 Nondifferentiable higher order symmetric duality under invexity/generalized invexity

Filomat ◽  
2014 ◽  
Vol 28 (8) ◽  
pp. 1661-1674 ◽  
Author(s):  
T.R. Gulati ◽  
Khushboo Verma
Keyword(s):  
Higher Order ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Converse Duality ◽  
Generalized Invexity ◽  
Self Duality ◽  
Special Cases ◽  
Dual Models

In this paper, we introduce a pair of nondifferentiable higher-order symmetric dual models. Weak, strong and converse duality theorems for this pair are established under the assumption of higher order invexity/generalized invexity. Self duality has been discussed assuming the function involved to be skew-symmetric. Several known results are obtained as special cases.

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.

Sign in / Sign up

Export Citation Format

Share Document