Duality in Multiobjective Optimization Problems with Set Constraints

2006 ◽  
pp. 131-146 ◽  
Author(s):  
Riccardo Cambini ◽  
Laura Carosi
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Set Constraints ◽  
Multiobjective Optimization Problems

scholarly journals Nonemptiness and Compactness of Solutions Set for Nondifferentiable Multiobjective Optimization Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Xin-kun Wu ◽  
Jia-wei Chen ◽  
Yun-zhi Zou
Keyword(s):  
Fixed Point ◽  
Multiobjective Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Efficient Solutions ◽  
Multiobjective Optimization Problem ◽  
Weakly Efficient Solutions ◽  
Set Constraints ◽  
Multiobjective Optimization Problems ◽  
Problems And Solutions

A nondifferentiable multiobjective optimization problem with nonempty set constraints is considered, and the equivalence of weakly efficient solutions, the critical points for the nondifferentiable multiobjective optimization problems, and solutions for vector variational-like inequalities is established under some suitable conditions. Nonemptiness and compactness of the solutions set for the nondifferentiable multiobjective optimization problems are proved by using the FKKM theorem and a fixed-point theorem.

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 Robust neutrosophic programming approach for solving intuitionistic fuzzy multiobjective optimization problems

2021 ◽  
Author(s):  
Firoz Ahmad
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Practical Implication ◽  
Real Life ◽  
Future Research ◽  
Programming Approach ◽  
Solution Approach ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multiobjective Optimization Problems

AbstractThis study presents the modeling of the multiobjective optimization problem in an intuitionistic fuzzy environment. The uncertain parameters are depicted as intuitionistic fuzzy numbers, and the crisp version is obtained using the ranking function method. Also, we have developed a novel interactive neutrosophic programming approach to solve multiobjective optimization problems. The proposed method involves neutral thoughts while making decisions. Furthermore, various sorts of membership functions are also depicted for the marginal evaluation of each objective simultaneously. The different numerical examples are presented to show the performances of the proposed solution approach. A case study of the cloud computing pricing problem is also addressed to reveal the real-life applications. The practical implication of the current study is also discussed efficiently. Finally, conclusions and future research scope are suggested based on the proposed work.

scholarly journals Assessing the Performance of Interactive Multiobjective Optimization Methods

2021 ◽  
Vol 54 (4) ◽  
pp. 1-27
Author(s):  
Bekir Afsar ◽  
Kaisa Miettinen ◽  
Francisco Ruiz
Keyword(s):  
Multiobjective Optimization ◽  
Decision Maker ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Interactive Methods ◽  
Value Functions ◽  
Technical Aspects ◽  
Preference Information ◽  
Multiobjective Optimization Problems ◽  
Human Decision

Interactive methods are useful decision-making tools for multiobjective optimization problems, because they allow a decision-maker to provide her/his preference information iteratively in a comfortable way at the same time as (s)he learns about all different aspects of the problem. A wide variety of interactive methods is nowadays available, and they differ from each other in both technical aspects and type of preference information employed. Therefore, assessing the performance of interactive methods can help users to choose the most appropriate one for a given problem. This is a challenging task, which has been tackled from different perspectives in the published literature. We present a bibliographic survey of papers where interactive multiobjective optimization methods have been assessed (either individually or compared to other methods). Besides other features, we collect information about the type of decision-maker involved (utility or value functions, artificial or human decision-maker), the type of preference information provided, and aspects of interactive methods that were somehow measured. Based on the survey and on our own experiences, we identify a series of desirable properties of interactive methods that we believe should be assessed.

An improved proximal method with quasi-distance for nonconvex multiobjective optimization problem

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Fouzia Amir ◽  
Ali Farajzadeh ◽  
Jehad Alzabut
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Convergence Result ◽  
Proximal Method ◽  
Pareto Solution ◽  
Multiobjective Optimization Problems ◽  
Locally Lipschitz ◽  
The Cost ◽  
Constrained Multiobjective Optimization

Abstract Multiobjective optimization is the optimization with several conflicting objective functions. However, it is generally tough to find an optimal solution that satisfies all objectives from a mathematical frame of reference. The main objective of this article is to present an improved proximal method involving quasi-distance for constrained multiobjective optimization problems under the locally Lipschitz condition of the cost function. An instigation to study the proximal method with quasi distances is due to its widespread applications of the quasi distances in computer theory. To study the convergence result, Fritz John’s necessary optimality condition for weak Pareto solution is used. The suitable conditions to guarantee that the cluster points of the generated sequences are Pareto–Clarke critical points are provided.

Sign in / Sign up

Export Citation Format

Share Document