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A Method of Solution for Quadratic Programs

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  • C. E. Lemke

    (Rensselaer Polytechnic Institute, Troy, New York)

Abstract

This paper describes a method of minimizing a strictly convex quadratic functional of several variables constrained by a system of linear inequalities. The method takes advantage of strict convexity by first computing the absolute minimum of the functional. In the event that the values of the variables yielding the absolute minimum do not satisfy the constraints, an equivalent and simplified quadratic problem in the "Lagrange multipliers" is derived. An efficient algorithm is devised for the transformed problem, which leads to the solution in a finite number of applications. A numerical example illustrates the method.

Suggested Citation

  • C. E. Lemke, 1962. "A Method of Solution for Quadratic Programs," Management Science, INFORMS, vol. 8(4), pages 442-453, July.
    • Handle: RePEc:inm:ormnsc:v:8:y:1962:i:4:p:442-453
    DOI: 10.1287/mnsc.8.4.442
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    Cited by:

    1. Marta García-Bárzana & Ana Belén Ramos-Guajardo & Ana Colubi & Erricos J. Kontoghiorghes, 2020. "Multiple linear regression models for random intervals: a set arithmetic approach," Computational Statistics, Springer, vol. 35(2), pages 755-773, June.
    2. Paul Knottnerus, 2016. "On new variance approximations for linear models with inequality constraints," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(1), pages 26-46, February.
    3. Ben-Daya, M. & Al-Sultan, K. S., 1997. "A new penalty function algorithm for convex quadratic programming," European Journal of Operational Research, Elsevier, vol. 101(1), pages 155-163, August.
    4. Khattree, Ravindra, 1998. "Some practical estimation procedures for variance components," Computational Statistics & Data Analysis, Elsevier, vol. 28(1), pages 1-32, July.
    5. Akkeles, Arif A. & Balogh, Laszlo & Illes, Tibor, 2004. "New variants of the criss-cross method for linearly constrained convex quadratic programming," European Journal of Operational Research, Elsevier, vol. 157(1), pages 74-86, August.

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