scholarly journals GeodesicB-Preinvex Functions and Multiobjective Optimization Problems on Riemannian Manifolds

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Sheng-lan Chen ◽  
Nan-Jing Huang ◽  
Donal O'Regan
Keyword(s):  
Multiobjective Optimization ◽  
Riemannian Manifolds ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Properly Efficient Solution ◽  
Invex Functions ◽  
Multiobjective Optimization Problems ◽  
Dual Programming ◽  
Preinvex Functions ◽  
Primal And Dual

We introduce a class of functions called geodesicB-preinvex and geodesicB-invex functions on Riemannian manifolds and generalize the notions to the so-called geodesic quasi/pseudoB-preinvex and geodesic quasi/pseudoB-invex functions. We discuss the links among these functions under appropriate conditions and obtain results concerning extremum points of a nonsmooth geodesicB-preinvex function by using the proximal subdifferential. Moreover, we study a differentiable multiobjective optimization problem involving new classes of generalized geodesicB-invex functions and derive Kuhn-Tucker-type sufficient conditions for a feasible point to be an efficient or properly efficient solution. Finally, a Mond-Weir type duality is formulated and some duality results are given for the pair of primal and dual programming.

Generalized Convexity and Characterization of (Weak) Pareto-Optimality in Nonsmooth Multiobjective Optimization Problems

2015 ◽  
Vol 14 (04) ◽  
pp. 877-899 ◽  
Author(s):  
Majid Soleimani-Damaneh
Keyword(s):  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Nonsmooth Analysis ◽  
Generalized Convexity ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Sufficient Optimality Conditions ◽  
Differential Analysis ◽  
Multiobjective Optimization Problems ◽  
Nonsmooth Multiobjective Optimization

Efforts to characterize optimality in nonsmooth and/or nonconvex optimization problems have made rapid progress in the past four decades. Nonsmooth analysis, which refers to differential analysis in the absence of differentiability, has grown rapidly in recent years, and plays a vital role in functional analysis, information technology, optimization, mechanics, differential equations, decision making, etc. Furthermore, convexity has been increasingly important nowadays in the study of many pure and applied mathematical problems. In this paper, some new connections between three major fields, nonsmooth analysis, convex analysis, and optimization, are provided that will help to make these fields accessible to a wider audience. In this paper, at first, we address some newly reported and interesting applications of multiobjective optimization in Management Science and Biology. Afterwards, some sufficient conditions for characterizing the feasible and improving directions of nonsmooth multiobjective optimization problems are given, and using these results a necessary optimality condition is proved. The sufficient optimality conditions are given utilizing a generalized convexity notion. Establishing necessary and sufficient optimality conditions for nonsmooth fractional programming problems is the next aim of the paper. We follow the paper by studying (strictly) prequasiinvexity and pseudoinvexity. Finally, some connections between these notions as well as some applications of these concepts in optimization are given.

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.

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