Milan Hladík. Multiparametric linear programming: support set and optimal partition invariancy. Eur. J. Oper. Res., 202(1):25–31, 2010.
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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.
@article{Hla2010b,
author = "Milan Hlad\'{\i}k",
title = "Multiparametric linear programming: support set and optimal partition invariancy",
journal = "Eur. J. Oper. Res.",
fjournal = "European Journal of Operational Research",
volume = "202",
number = "1",
pages = "25-31",
year = "2010",
doi = "10.1016/j.ejor.2009.04.019",
bib2html_dl_html = "http://dx.doi.org/10.1016/j.ejor.2009.04.019",
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.",
keywords = "parametric programming, linear programming sensitivity analysis",
}
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