Analytic efficient solution set for multi-criteria quadratic programs

We present active set methods to evaluate the exact analytic efficient solution set for multi-criteria convex quadratic programming problems (MCQP) subject to linear constraints. The idea is based on the observations that a strictly convex programming problem admits a unique solution, and that the e...

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Bibliographic Details
Published in:European journal of operational research Vol. 92; no. 1; pp. 166 - 181
Main Authors: Goh, C.J., Yang, X.Q.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 05.07.1996
Elsevier
Elsevier Sequoia S.A
Series:European Journal of Operational Research
Subjects:
Active set methods
Analytic solution
Efficiency
Mathematical programming
Multiple criteria
Operations research
Quadratic programming
Studies
Multiple criteria
Analytic solution
Quadratic programming
Active set methods
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:We present active set methods to evaluate the exact analytic efficient solution set for multi-criteria convex quadratic programming problems (MCQP) 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.
Bibliography:ObjectType-Article-1
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ISSN:0377-2217
1872-6860
DOI:10.1016/0377-2217(95)00040-2