Piecewise quadratic approximation of the non-dominated set for bi-criteria programs

Piecewise quadratic approximation of the non-dominated set for bi-criteria programs

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Article ID: iaor20023477
Country: United Kingdom
Volume: 10
Issue: 1
Start Page Number: 35
End Page Number: 47
Publication Date: Jan 2001
Journal: Journal of Multi-Criteria Decision Analysis
Authors: , ,
Keywords: programming: quadratic
Abstract:

A procedure to approximate the non-dominated set for general (continuous) bi-criteria programs is proposed. The piecewise approximation is composed of quadratic curves, each of which is developed locally in a neighbourhood of a non-dominated point of interest and based on primal–dual relationships associated with the weighted Tchebycheff scalarization of the original problem. The approximating quadratic functions, in which decision maker's preferences are represented, give a closed-form description of the non-dominated set. A numerical example is included.

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