Utility Function Programs and Optimization over the Efficient Set in Multiple-Objective Decision Making

R. Horst and N. V. Thoai
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R. Horst: University of Trier
N. V. Thoai: Institute of Mathematics, Bo Ho

Journal of Optimization Theory and Applications, 1997, vol. 92, issue 3, No 8, 605-631

Abstract: 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.

Keywords: Multiple-objective optimization; utility function programs; global optimization; branch-and-bound algorithms (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (10)

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DOI: 10.1023/A:1022659523991

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