Analytic efficient solution set for multi-criteria quadratic programs

Analytic efficient solution set for multi-criteria quadratic programs

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Article ID: iaor1999421
Country: Netherlands
Volume: 92
Issue: 1
Start Page Number: 166
End Page Number: 181
Publication Date: Jul 1996
Journal: European Journal of Operational Research
Authors: ,
Keywords: programming: multiple criteria
Abstract:

We present active set methods to evaluate the exact analytic efficient solution set for multi-criteria convex quadratic programming problems subject to linear constraints. The idea is based on the observations that a strictly convex programming problem admits a unique solution, and that the efficient solution set for a multi-criteria strictly convex quadratic programming problem with linear equality constraints can be parameterized. The case of bi-criteria quadratic programming (BCQP) is first discussed since many of the underlying ideas can be explained much more clearly in the case of two objectives. In particular we note that the efficient solution set of a BCQP problem is a curve on the surface of a polytope. The extension to problems with more than two objectives is straightforward albeit some slightly more complicated notation. Two numerical examples are given to illustrate the proposed methods.

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