Analytic efficient solution set for multi-criteria quadratic programs

C. J. Goh, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

19 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)166-181
Number of pages16
JournalEuropean Journal of Operational Research
Issue number1
Publication statusPublished - 5 Jul 1996
Externally publishedYes


  • Active set methods
  • Analytic solution
  • Multiple criteria
  • Quadratic programming

ASJC Scopus subject areas

  • Modelling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


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