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Saturation in Linear Optimization

Author

Listed:
  • M.A. Goberna

    (University of Alicante)

  • V. Jornet

    (University of Alicante)

  • M. Molina

    (University of Alicante)

Abstract

In a solvable linear optimization problem, a constraint is saturated if it is binding at a certain optimal solution and it is weakly saturated if it is binding at a proper subset of the optimal set. Nonsaturation and weak saturation can be seen as redundancy phenomena in the sense that the elimination of a finite number of these constraints preserves the value of the given problem. We consider also the effect of sufficiently small perturbations of the cost coefficients in the classification of a given constraint as either saturated or nonsaturated.

Suggested Citation

  • M.A. Goberna & V. Jornet & M. Molina, 2003. "Saturation in Linear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 117(2), pages 327-348, May.
    • Handle: RePEc:spr:joptap:v:117:y:2003:i:2:d:10.1023_a:1023683723813
    DOI: 10.1023/A:1023683723813
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    References listed on IDEAS

    as
    1. J. C. G. Boot, 1962. "On Trivial and Binding Constraints in Programming Problems," Management Science, INFORMS, vol. 8(4), pages 419-441, July.
    2. Gerald L. Thompson & Fred M. Tonge & Stanley Zionts, 1966. "Techniques for Removing Nonbinding Constraints and Extraneous Variables from Linear Programming Problems," Management Science, INFORMS, vol. 12(7), pages 588-608, March.
    3. Rubén Puente & Virginia Vera de Serio, 1999. "Locally Farkas-Minkowski linear inequality systems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(1), pages 103-121, June.
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