Utility Function Programs and Optimization over the Efficient Set in Multiple-Objective Decision Making |
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Authors: | R Horst N V Thoai |
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Institution: | (1) Fachbereich IV—Department of Mathematics, University of Trier, Trier, Germany;(2) Institute of Mathematics, Bo Ho, Hanoi, Vietnam;;(3) Fachbereich IV—Department of Mathematics, University of Trier, Trier, Germany |
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Abstract: | Natural basic concepts in multiple-objective optimization lead to difficult multiextremal global optimization problems. Examples include detection of efficient points when nonconvexities occur, and optimization of a linear function over the efficient set in the convex (even linear) case. Assuming that a utility function exists allows one to replace in general the multiple-objective program by a single, nonconvex optimization problem, which amounts to a minimization over the efficient set when the utility function is increasing. A new algorithm is discussed for this utility function program which, under natural mild conditions, converges to an -approximate global solution in a finite number of iterations. Applications include linear, convex, indefinite quadratic, Lipschitz, and d.c. objectives and constraints. |
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Keywords: | Multiple-objective optimization utility function programs global optimization branch-and-bound algorithms |
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