Newton method to obtain efficient solutions of the optimization problems with interval-valued objective functions

2016 ◽  
Vol 53 (1-2) ◽  
pp. 709-731 ◽  
Author(s):  
Debdas Ghosh
Keyword(s):  
Newton Method ◽  
Optimization Problems ◽  
Efficient Solutions ◽  
Objective Functions ◽  
Interval Valued

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.

A Newton method for capturing Pareto optimal solutions of fuzzy multiobjective optimization problems

2019 ◽  
Vol 53 (3) ◽  
pp. 867-886
Author(s):  
Mehrdad Ghaznavi ◽  
Narges Hoseinpoor ◽  
Fatemeh Soleimani
Keyword(s):  
Multiobjective Optimization ◽  
Newton Method ◽  
Optimization Problems ◽  
Order Relation ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Multiobjective Optimization Problems ◽  
Generalized Hukuhara Differentiability

In this study, a Newton method is developed to obtain (weak) Pareto optimal solutions of an unconstrained multiobjective optimization problem (MOP) with fuzzy objective functions. For this purpose, the generalized Hukuhara differentiability of fuzzy vector functions and fuzzy max-order relation on the set of fuzzy vectors are employed. It is assumed that the objective functions of the fuzzy MOP are twice continuously generalized Hukuhara differentiable. Under this assumption, the relationship between weakly Pareto optimal solutions of a fuzzy MOP and critical points of the related crisp problem is discussed. Numerical examples are provided to demonstrate the efficiency of the proposed methodology. Finally, the convergence analysis of the method under investigation is discussed.

scholarly journals Interval-Valued Vector Optimization Problems Involving Generalized Approximate Convexity

2020 ◽  
Author(s):  
Mohsine Jennane ◽  
Lhoussain El Fadil ◽  
El Mostafa Kalmoun
Keyword(s):  
Variational Inequality ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Efficient Solutions ◽  
Vector Optimization Problems ◽  
Sufficient Optimality Conditions ◽  
Approximate Convexity ◽  
Study Interval ◽  
Necessary And Sufficient ◽  
Interval Valued

Interval-valued functions have been widely used to accommodate data inexactness in optimization and decision theory. In this paper, we study interval-valued vector optimization problems, and derive their relationships to interval variational inequality problems, of both Stampacchia and Minty types. Using the concept of interval approximate convexity, we establish necessary and sufficient optimality conditions for local strong quasi and approximate $LU$-efficient solutions to nonsmooth optimization problems with interval-valued multiobjective functions.

scholarly journals Approximate-Karush-Kuhn-Tucker Conditions and Interval Valued Vector Variational Inequalities

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Optimality Conditions ◽  
Optimization Problems ◽  
Vector Variational Inequality ◽  
Vector Variational Inequalities ◽  
Variational Inequality Problems ◽  
Objective Functions ◽  
Interval Valued

This Article deals with the Approximate Karush-Kuhn-Tucker (AKKT) optimality conditions for interval valued multiobjective function as a generalization of Karush-Kuhn-Tucker optimality conditions. Further, we establish relationship between vector variational inequality problems and multiobjective interval valued optimization problems under the assumption of LU−convex smooth and nonsmooth objective functions.

Optimization of the mathematical programming and applications

2021 ◽  
Vol 2 (5) ◽  
pp. 7902-7911
Author(s):  
Johnny Moisés Valverde Montoro ◽  
Milton Milciades Cortez Gutiérrez ◽  
Hernán Oscar Cortez Gutiérrez
Keyword(s):  
Mathematical Programming ◽  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Optimization Problems ◽  
Kkt Conditions ◽  
Objective Functions ◽  
Multiobjective Optimization Problems ◽  
Interval Valued

The present investigation responds to the need to solve optimization problems with optimality conditions. The KKT conditions are considered for multiobjective optimization problems with interval-valued objective functions.

Scalable Computing Architecture for Time-Dependent Transportation Optimization Problems Based on High-Performance Computing Techniques

2019 ◽  
Vol 2673 (4) ◽  
pp. 205-216 ◽  
Author(s):  
Pengfei (Taylor) Li ◽  
Peirong (Slade) Wang ◽  
Farzana Chowdhury ◽  
Li Zhang
Keyword(s):  
Objective Function ◽  
High Performance Computing ◽  
High Performance ◽  
Optimization Problems ◽  
Dynamic Network ◽  
Alternative Formulation ◽  
High Fidelity ◽  
Objective Functions ◽  
Performance Computing ◽  
Transportation Optimization

Traditional formulations for transportation optimization problems mostly build complicating attributes into constraints while keeping the succinctness of objective functions. A popular solution is the Lagrangian decomposition by relaxing complicating constraints and then solving iteratively. Although this approach is effective for many problems, it generates intractability in other problems. To address this issue, this paper presents an alternative formulation for transportation optimization problems in which the complicating attributes of target problems are partially or entirely built into the objective function instead of into the constraints. Many mathematical complicating constraints in transportation problems can be efficiently modeled in dynamic network loading (DNL) models based on the demand–supply equilibrium, such as the various road or vehicle capacity constraints or “IF–THEN” type constraints. After “pre-building” complicating constraints into the objective functions, the objective function can be approximated well with customized high-fidelity DNL models. Three types of computing benefits can be achieved in the alternative formulation: ( a) the original problem will be kept the same; ( b) computing complexity of the new formulation may be significantly reduced because of the disappearance of hard constraints; ( c) efficiency loss on the objective function side can be mitigated via multiple high-performance computing techniques. Under this new framework, high-fidelity and problem-specific DNL models will be critical to maintain the attributes of original problems. Therefore, the authors’ recent efforts in enhancing the DNL’s fidelity and computing efficiency are also described in the second part of this paper. Finally, a demonstration case study is conducted to validate the new approach.

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