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Constraint Aggregation Principle in Convex Optimization

Author

Listed:
  • Y.M. Ermoliev
  • A.V. Kryazhimskii
  • A. Ruszczynski

Abstract

A general constraint aggregation technique is proposed for convex optimization problems. At each iteration a set of convex inequalities and linear equations is replaced by a single inequality formed as a linear combination of the original constraints. After solving the simplified subproblem, new aggregation coefficients are calculated and the iteration continues. This general aggregation principle is incorporated into a number of specific algorithms. Convergence of the new methods is proved and speed of convergence analyzed. It is shown that in case of linear programming, the method with aggregation has a polynomial complexity. Finally, application to decomposable problems is discussed.

Suggested Citation

  • Y.M. Ermoliev & A.V. Kryazhimskii & A. Ruszczynski, 1995. "Constraint Aggregation Principle in Convex Optimization," Working Papers wp95015, International Institute for Applied Systems Analysis.
    • Handle: RePEc:wop:iasawp:wp95015
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    References listed on IDEAS

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    1. David F. Rogers & Robert D. Plante & Richard T. Wong & James R. Evans, 1991. "Aggregation and Disaggregation Techniques and Methodology in Optimization," Operations Research, INFORMS, vol. 39(4), pages 553-582, August.
    2. Fred Glover, 1975. "Surrogate Constraint Duality in Mathematical Programming," Operations Research, INFORMS, vol. 23(3), pages 434-451, June.
    3. Andrzej Ruszczyński, 1987. "A Linearization Method for Nonsmooth Stochastic Programming Problems," Mathematics of Operations Research, INFORMS, vol. 12(1), pages 32-49, February.
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    Cited by:

    1. Y.M. Ermoliev & A. Ruszczynski, 1995. "Convex Optimization by Radial Search," Working Papers wp95036, International Institute for Applied Systems Analysis.
    2. M. K. H. Fan & Y. Gong, 1999. "Exterior Minimum-Penalty Path-Following Methods in Semidefinite Programming," Journal of Optimization Theory and Applications, Springer, vol. 100(2), pages 327-348, February.
    3. B.V. Digas & Y.M. Ermoliev & A.V. Kryazhimskii, 1998. "Guaranteed Optimization in Insurance of Catastrophic Risks," Working Papers ir98082, International Institute for Applied Systems Analysis.
    4. R. Rozycki, 1995. "Constraint Aggregation Principle: Application to a Dual Transportation Problem," Working Papers wp95103, International Institute for Applied Systems Analysis.
    5. M. Davidson, 1996. "Proximal Point Mappings and Constraint Aggregation Principle," Working Papers wp96102, International Institute for Applied Systems Analysis.
    6. A.V. Kryazhimskii & V.I. Maksimov & Yu.S. Osipov, 1996. "Reconstruction of Boundary Sources through Sensor Observations," Working Papers wp96097, International Institute for Applied Systems Analysis.
    7. A.V. Kryazhimskii & A. Ruszczynski, 1997. "Constraint Aggregation in Infinite-Dimensional Spaces and Applications," Working Papers ir97051, International Institute for Applied Systems Analysis.

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