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Comparison of methods for solving sets of linear inequalities in the bounded-error context

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  • Piet-Lahanier, Hélène
  • Veres, Sándor M.
  • Walter, Eric

Abstract

Effective recursive updating of the solution set of linear inequalities has recently gained importance in the area of parameter bounding for system identification, prediction and control. When it is not empty, this solution set is a convex polyhedron, usually a convex polytope in the context of parameter bounding. Several algorithms have been proposed in the literature to update this polyhedron when a new inequality is introduced. This paper describes three of them in a unified framework and compares them on the number of operations involved and the memory space required.

Suggested Citation

  • Piet-Lahanier, Hélène & Veres, Sándor M. & Walter, Eric, 1992. "Comparison of methods for solving sets of linear inequalities in the bounded-error context," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 34(6), pages 515-524.
    • Handle: RePEc:eee:matcom:v:34:y:1992:i:6:p:515-524
    DOI: 10.1016/0378-4754(92)90038-I
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    References listed on IDEAS

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    1. Walter, Eric & Piet-Lahanier, Hélène, 1990. "Estimation of parameter bounds from bounded-error data: a survey," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 449-468.
    2. T. H. Matheiss & David S. Rubin, 1980. "A Survey and Comparison of Methods for Finding All Vertices of Convex Polyhedral Sets," Mathematics of Operations Research, INFORMS, vol. 5(2), pages 167-185, May.
    3. Mo, S.H. & Norton, J.P., 1990. "Fast and robust algorithm to compute exact polytope parameter bounds," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 481-493.
    4. Broman, V. & Shensa, M.J., 1990. "A compact algorithm for the intersection and approximation of N-dimensional polytopes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 469-480.
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