Proper efficiency and the theory of vector maximization
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In this paper, the concept of proper efficiency was introduced to eliminate efficient points of a certain anomalous nature in the problem of vector maximization, which is related in spirit to the notion of "proper" efficiency introduced by Kuhn and Tucker in their celebrated paper of 1950.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 1968-06-01 and is currently open access. It has received 1272 citations till now. The article focuses on the topics: Decision rule & Decision theory.read more
Citations
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Survey of multi-objective optimization methods for engineering
R.T. Marler,Jasbir S. Arora +1 more
TL;DR: A survey of current continuous nonlinear multi-objective optimization concepts and methods finds that no single approach is superior and depends on the type of information provided in the problem, the user's preferences, the solution requirements, and the availability of software.
Book
Metaheuristics: From Design to Implementation
TL;DR: This book provides a complete background on metaheuristics and shows readers how to design and implement efficient algorithms to solve complex optimization problems across a diverse range of applications, from networking and bioinformatics to engineering design, routing, and scheduling.
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The weighted sum method for multi-objective optimization: new insights
TL;DR: This paper investigates the fundamental significance of the weights in terms of preferences, the Pareto optimal set, and objective-function values and determines the factors that dictate which solution point results from a particular set of weights.
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Theory of Vector Optimization
Christiane Tammer,Alfred Göpfert +1 more
TL;DR: This work derives necessary and sufficient optimality conditions, a minimal point theorem, a vector-valued variational principle of Ekeland’s type, Lagrangean multiplier rules and duality statements, and discusses a general scalarization procedure.
References
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Strictly Concave Parametric Programming, Part I: Basic Theory
TL;DR: This paper, which is presented in two parts, develops a computational approach to strictly concave parametric programs of the form: Maximize α f1x + 1-αf2x subject to concave inequality constraints for each fixed value of α in the unit interval, where f1 and f2 are strictly Concave and certain additional regularity conditions are satisfied.
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Strictly Concave Parametric Programming, Part II: Additional Theory and Computational Considerations
TL;DR: The theory presented in Part I of this paper led to a Basic Parametric Procedure for a broad class of strictly concave parametric programs as mentioned in this paper, which facilitates efficient computational implementation.