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 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 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 Class of Isoperimetric Constrained Controlled Optimization Problems

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 112
Author(s):  
Savin Treanţă
Keyword(s):  
Boundary Conditions ◽  
Control Problem ◽  
Optimality Conditions ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Control Problems ◽  
Integral Functionals ◽  
Curvilinear Integral ◽  
The One ◽  
Theoretical Results

In this paper, we investigate the Lagrange dynamics generated by a class of isoperimetric constrained controlled optimization problems involving second-order partial derivatives and boundary conditions. More precisely, we derive necessary optimality conditions for the considered class of variational control problems governed by path-independent curvilinear integral functionals. Moreover, the theoretical results presented in the paper are accompanied by an illustrative example. Furthermore, an algorithm is proposed to emphasize the steps to be followed to solve a control problem such as the one studied in this paper.

scholarly journals Duality theorems for nondifferentiable semi-infinite interval-valued optimization problems with vanishing constraints

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Haijun Wang ◽  
Huihui Wang
Keyword(s):  
Optimization Problem ◽  
Generalized Convexity ◽  
Optimization Problems ◽  
Strong Duality ◽  
Infinite Interval ◽  
Duality Theorems ◽  
Converse Duality ◽  
Vanishing Constraints ◽  
Dual Models ◽  
Interval Valued

AbstractIn this paper, we study the duality theorems of a nondifferentiable semi-infinite interval-valued optimization problem with vanishing constraints (IOPVC). By constructing the Wolfe and Mond–Weir type dual models, we give the weak duality, strong duality, converse duality, restricted converse duality, and strict converse duality theorems between IOPVC and its corresponding dual models under the assumptions of generalized convexity.

scholarly journals On Robust Saddle-Point Criterion in Optimization Problems with Curvilinear Integral Functionals

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1790
Author(s):  
Savin Treanţă ◽  
Koushik Das
Keyword(s):  
Saddle Point ◽  
Optimization Problems ◽  
Integral Functional ◽  
Optimal Solution ◽  
Control Problems ◽  
New Class ◽  
Mixed Constraints ◽  
Curvilinear Integral ◽  
Lagrange Functional ◽  
Cost Functionals

In this paper, we introduce a new class of multi-dimensional robust optimization problems (named (P)) with mixed constraints implying second-order partial differential equations (PDEs) and inequations (PDIs). Moreover, we define an auxiliary (modified) class of robust control problems (named (P)(b¯,c¯)), which is much easier to study, and provide some characterization results of (P) and (P)(b¯,c¯) by using the notions of normal weak robust optimal solution and robust saddle-point associated with a Lagrange functional corresponding to (P)(b¯,c¯). For this aim, we consider path-independent curvilinear integral cost functionals and the notion of convexity associated with a curvilinear integral functional generated by a controlled closed (complete integrable) Lagrange 1-form.

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 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 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.

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