Characterizing the nondominated set by separable functions
type: Item
instance of: scholarly article
title: Characterizing the nondominated set by separable functions
zbMATH Open document ID: 0628.90077
DOI: 10.1007/BF00940308
author: Mordecai Henig
published in: Journal of Optimization Theory and Applications
publication date: 1988-01-01T00:00:00Z
review text: We present sufficient and necessary conditions for classes of separable (additive) functions to generate the set of nondominated outcomes in multicriteria optimization problems. The basic technique consists of convexifying the set of outcomes and then to apply the standard characterization of a convex set by a class of linear functions. The conditions include the case when the set of feasible alternatives is convex and the criteria are convex-transformable. We show that the sum of powers and the sum of exponents functions can generate the nondominated set for an arbitrary set of outcomes (under compactness conditions). We also discuss monotonicity, proper nondominance, uniqueness and connectedness of solutions, and weights and tradeoffs with respect to these functions.
Mathematics Subject Classification ID: 90C31
zbMATH DE Number: 4023043
zbMATH Keywords: Pareto sets
zbMATH Keywords: separable functions
zbMATH Keywords: nondominated outcomes
zbMATH Keywords: multicriteria optimization
MaRDI profile type: Publication
cites work: Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives
cites work: Proper efficiency with respect to cones
cites work: An improved definition of proper efficiency for vector maximization with respect to cones
cites work: Proper efficiency and the theory of vector maximization
cites work: A Class of Solutions for Group Decision Problems
cites work: Compromise solutions, domination structures, and Salukvadze's solution
cites work: Optimization of vector functionals. I. The programming of optimal trajectories
cites work: Note on the mean-square strategy for vector-valued objective functions
cites work: On a Bicriterion Formulation of the Problems of Integrated System Identification and System Optimization
cites work: Technical Note—Parametric Solution of a Class of Nonconvex Programs
cites work: Vector maximization with two objective functions
cites work: Compromise solutions and estimation of the noninferior set
cites work: Scalarization in vector optimization
cites work: Some characterizations of the optimal solutions of a vector optimization problem
cites work: Characterization of properly efficient solutions by generalized scalarization methods
cites work: On Cone-Efficiency, Cone-Convexity and Cone-Compactness
cites work: Proper Efficient Points for Maximizations with Respect to Cones
cites work: State Constraints in Convex Control Problems of Bolza
cites work: Q4135211
cites work: Connectedness of the set of nondominated outcomes in multicriteria optimization
cites work: Quasiconcave vector maximization: Connectedness of the sets of Pareto- optimal and weak Pareto-optimal alternatives
cites work: Q3760254
full work available at URL: https://doi.org/10.1007/bf00940308
OpenAlex ID: W2091078743
description: scientific article; zbMATH DE number 4023043