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An Algorithm for the Solution of a Quadratic Programming Problem, with Application to Constrained Matrix and Spatial Price Equilibrium Problems

Author

Listed:
  • A Nagurney

    (Department of General Business and Finance, School of Management, University of Massachusetts, Amherst, MA 01003, USA)

  • Referee H K Chen

    (2230 Newmark Civil Engineering Laboratory, 205 North Mathews Avenue, Urbana, IL 61801, USA)

Abstract

In this paper a quadratic programming problem is considered. It contains, as special cases, formulations of constrained matrix problems with unknown row and column totals, and classical spatial price equilibrium problems with congestion. An equilibration algorithm, which is of the relaxation type, is introduced into the problem. It resolves the system into subproblems, which in turn, can be solved exactly, even in the presence of upper bounds. Also provided is computational experience for several large-scale examples. This work identifies the equivalency between constrained matrix problems and spatial price equilibrium problems which had been postulated, but, heretofore, not made.

Suggested Citation

  • A Nagurney & Referee H K Chen, 1989. "An Algorithm for the Solution of a Quadratic Programming Problem, with Application to Constrained Matrix and Spatial Price Equilibrium Problems," Environment and Planning A, , vol. 21(1), pages 99-114, January.
    • Handle: RePEc:sae:envira:v:21:y:1989:i:1:p:99-114
    DOI: 10.1068/a210099
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    References listed on IDEAS

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    1. Erlander, Sven & Jörnsten, Kurt O. & Lundgren, Jan T., 1985. "On the estimation of trip matrices in the case of missing and uncertain data," Transportation Research Part B: Methodological, Elsevier, vol. 19(2), pages 123-141, April.
    2. Hewings, Geoffrey J. D., 1984. "The role of prior information in updating regional input-output models," Socio-Economic Planning Sciences, Elsevier, vol. 18(5), pages 319-336.
    3. Dwight Freund & Umesh Saxena, 1984. "Technical Note—An Algorithm for a Class of Discrete Maximum Entropy Problems," Operations Research, INFORMS, vol. 32(1), pages 210-215, February.
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