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 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 On nonsmooth mathematical programs with equilibrium constraints using generalized convexity

2019 ◽  
Vol 29 (4) ◽  
pp. 449-463
Author(s):  
Bhuwan Joshi ◽  
Shashi Mishra ◽  
P Pankaj
Keyword(s):  
Generalized Convexity ◽  
Mathematical Program ◽  
Strong Duality ◽  
Global Optimality ◽  
Sufficient Condition ◽  
Equilibrium Constraints ◽  
Duality Theorems ◽  
Generalized Invexity ◽  
Mathematical Programs ◽  
Dual Models

In this paper, we derive the sufficient condition for global optimality for a nonsmooth mathematical program with equilibrium constraints involving generalized invexity. We formulate the Wolfe and Mond-Weir type dual models for the problem using convexificators. We establish weak and strong duality theorems to relate the mathematical program with equilibrium constraints and the dual models in the framework of convexificators.

scholarly journals Generalized invexity and mathematical programs

2020 ◽  
pp. 35-35
Author(s):  
Bhuwan Joshi ◽  
Rakesh Mohan ◽  
P Pankaj
Keyword(s):  
Generalized Convexity ◽  
Strong Duality ◽  
Mathematical Programming Problem ◽  
Stationary Condition ◽  
Local Optimality ◽  
Equilibrium Constraints ◽  
Duality Theorems ◽  
Mathematical Programs ◽  
Convexity Assumptions ◽  
Dual Models

In this paper, using generalized convexity assumptions, we show that M- stationary condition is sufficient for global or local optimality under some mathematical programming problem with equilibrium constraints(MPEC). Further, we formulate and study Wolfe type and Mond-Weir type dual models for the MPEC, and we establish weak and strong duality theorems.

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 Mixed E-duality for E-differentiable Vector Optimization Problems Under (Generalized) V-E-invexity

2021 ◽  
Vol 2 (3) ◽  
Author(s):  
Najeeb Abdulaleem
Keyword(s):  
Vector Optimization ◽  
Optimization Problem ◽  
Dual Problem ◽  
Optimization Problems ◽  
Vector Optimization Problem ◽  
Equality Constraints ◽  
Vector Optimization Problems ◽  
Duality Theorems ◽  
Differentiable Vector

AbstractIn this paper, a class of E-differentiable vector optimization problems with both inequality and equality constraints is considered. The so-called vector mixed E-dual problem is defined for the considered E-differentiable vector optimization problem with both inequality and equality constraints. Then, several mixed E-duality theorems are established under (generalized) V-E-invexity hypotheses.

On quasi approximate solutions for nonsmooth robust semi-infinite optimization problems

2019 ◽  
Vol 35 (3) ◽  
pp. 417-426 ◽  
Author(s):  
CHANOKSUDA KHANTREE ◽  
RABIAN WANGKEEREE ◽  
◽  
Keyword(s):  
Constraint Qualification ◽  
Generalized Convexity ◽  
Optimization Problems ◽  
Approximate Solutions ◽  
Data Uncertainty ◽  
Necessary Condition ◽  
Duality Theorems ◽  
Approximate Form ◽  
Locally Lipschitz ◽  
Approximate Duality

This paper devotes to the quasi ε-solution for robust semi-infinite optimization problems (RSIP) involving a locally Lipschitz objective function and infinitely many locally Lipschitz constraint functions with data uncertainty. Under the fulfillment of robust type Guignard constraint qualification and robust type Kuhn-Tucker constraint qualification, a necessary condition for a quasi ε-solution to problem (RSIP). After introducing the generalized convexity, we give a sufficient optimality for such a quasi ε-solution to problem (RSIP). Finally, we also establish approximate duality theorems in term of Wolfe type which is formulated in approximate form.

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 Approximate proper efficiency for multiobjective optimization problems

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 6091-6101
Author(s):  
Ying Gao ◽  
Zhihui Xu
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problem ◽  
Normal Cone ◽  
Generalized Convexity ◽  
Optimization Problems ◽  
Proper Efficiency ◽  
Proximal Normal Cone ◽  
Radiant Set ◽  
Benson Proper Efficiency ◽  
Multiobjective Optimization Problems

This paper is devoted to the study of a new kind of approximate proper efficiency in terms of proximal normal cone and co-radiant set for multiobjective optimization problem. We derive some properties of the new approximate proper efficiency and discuss the relations with the existing approximate concepts, such as approximate efficiency and approximate Benson proper efficiency. At last, we study the linear scalarizations for the new approximate proper efficiency under the generalized convexity assumption and give some examples to illustrate the main results.

Sign in / Sign up

Export Citation Format

Share Document