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Multiparametric linear programming: Support set and optimal partition invariancy

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  • Hladík, Milan

Abstract

Traditional sensitivity and parametric analysis in linear optimization was based on preserving optimal basis. Interior point methods, however, do not converge to a basic solution (vertex) in general. Recently, there appeared new techniques in sensitivity analysis, which consist in preserving so called support set invariancy and optimal partition invariancy. This paper reflects the renascence of sensitivity and parametric analysis and extends single-parametric results to the case when there are multiple parameters in the objective function and in the right-hand side of equations. Multiparametric approach enables us to study more complex perturbation occurring in linear programs than the simpler sensitivity analysis does. We present a description of the set of admissible parameters under the mentioned invariances, and compare them with the classical optimal basis concept.

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  • Hladík, Milan, 2010. "Multiparametric linear programming: Support set and optimal partition invariancy," European Journal of Operational Research, Elsevier, vol. 202(1), pages 25-31, April.
    • Handle: RePEc:eee:ejores:v:202:y:2010:i:1:p:25-31
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    References listed on IDEAS

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    1. F. Borrelli & A. Bemporad & M. Morari, 2003. "Geometric Algorithm for Multiparametric Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 118(3), pages 515-540, September.
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    Cited by:

    1. Hladík, Milan & Sitarz, Sebastian, 2013. "Maximal and supremal tolerances in multiobjective linear programming," European Journal of Operational Research, Elsevier, vol. 228(1), pages 93-101.
    2. Ma, Kang-Ting & Lin, Chi-Jen & Wen, Ue-Pyng, 2013. "Type II sensitivity analysis of cost coefficients in the degenerate transportation problem," European Journal of Operational Research, Elsevier, vol. 227(2), pages 293-300.
    3. Borgonovo, Emanuele & Buzzard, Gregery T. & Wendell, Richard E., 2018. "A global tolerance approach to sensitivity analysis in linear programming," European Journal of Operational Research, Elsevier, vol. 267(1), pages 321-337.

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