A further study on inverse linear programming problems.

*(English)*Zbl 0971.90051Summary: The authors continue their previous study [J. Comput. Appl. Math. 72, 261-273 (1996; Zbl 0856.65069)] on inverse linear programming problems which requires us to adjust the cost coefficients of a given LP problem as less as possible so that a known feasible solution becomes the optimal one. In particular, they consider the cases in which the given feasible solution and one optimal solution of the LP problem are 0-1 vectors which often occur in network programming and combinatorial optimization, and give very simple methods for solving this type of inverse LP problems. Besides, instead of the commonly used \(l_1\) measure, they also consider the inverse LP problems under \(l_\infty\) measure and propose solution methods.

##### MSC:

90C08 | Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.) |

90C27 | Combinatorial optimization |

52A20 | Convex sets in \(n\) dimensions (including convex hypersurfaces) |

52B12 | Special polytopes (linear programming, centrally symmetric, etc.) |

65K05 | Numerical mathematical programming methods |

##### Software:

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\textit{J. Zhang} and \textit{Z. Liu}, J. Comput. Appl. Math. 106, No. 2, 345--359 (1999; Zbl 0971.90051)

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##### References:

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