Postoptimal Analysis of a Linear Program under Simultaneous Changes in Matrix Coefficients

  • Robert M .
  • Published 1984

Abstract

This paper examines the sensitivity of a linear program to simultaneous changes in matrix coefficients. Consider a linear program whose coefficient matrix depends linearly on a scalar parameter 0. Previous research has attempted to express the optimal objective value z(O) of the problem, as well as solutions to the primal and dual, as ratios of polynomial functions of 0 over a range of 0. Herein, we study properties of z(O) and the associated optimal basic feasible solution in a neighborhood about a fixed value 0 of 0. We obtain readily computable formulas for the Taylor series' (and hence all derivatives) of z(0) and of the primal and dual optimal basic solutions about the point /~ Furthermore, even under degeneracy, we show how to determine whether or not 0 is one of finitely many possible values of 0 for which derivatives of z(O) may not exist, by examining the lexicographic order of a certain matrix. This test also reveals whether or not the formulas given represent left-sided and/or right-sided derivatives of z(O) at

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Cite this paper

@inproceedings{1984PostoptimalAO, title={Postoptimal Analysis of a Linear Program under Simultaneous Changes in Matrix Coefficients}, author={Robert M .}, year={1984} }