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On some aspects of the matrix data perturbation in linear program. (English) Zbl 1138.90426

The most of the previous authors consider linear programming (LP) problems, where only one coefficient, a row (column), or few rows (columns) are linear functions of a parameter. This one deals with a more general case, when all the coefficients are polynomial functions of the parameter \(t\in T\subseteq \mathbb R\). For such problems, assuming that some nonsingularity conditions hold and an optimal base matrix is known for some particular value \(\bar t\) of the parameter, corresponding explicit optimal basic solution in the neigbourhood of \(\bar t\) is determined by solving an augmented LP problem with real system matrix coefficients. Parametric LP can be used, for instance, to model the production problem, where technology, resources, costs and similar categories vary with time.

MSC:

90C05 Linear programming
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