| DEGENERATE OPTIMAL BASIS GRAPHS IN LINEAR PROGRAMMING |
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| 作者姓名： | Lin Yixun\ Wen JianjunDept.of Math. Zhengzhou Univ. Zhengzhou . |
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| 作者单位： | Lin Yixun\ Wen JianjunDept.of Math.，Zhengzhou Univ.，Zhengzhou450 0 52 . |
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| 基金项目： | Project supported by the National Natural Science Foundation of China!(19771075) |
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| 摘 要： | § 1 IntroductionA graph-theoretic approach for investigating basis transformations in a linear pro-gramming has been historically developed.Let V be the setof all bases with respectto thecolumn vectors of a matrix A.Two bases are called adjacentifthey can be transformed intoeach other by a pivot operation.Denote by E the set of edges each of which is incidentwith a pair of adjacentbases.Then G=(V,E) is called the basisgraph of matrix A(or ofthe corresponding LP) .Tucker1 ] first called…
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DEGENERATE OPTIMAL BASIS GRAPHS IN LINEAR PROGRAMMING |
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| Lin Yixun\ Wen JianjunDept.of Math.,Zhengzhou Univ.,Zhengzhou ..DEGENERATE OPTIMAL BASIS GRAPHS IN LINEAR PROGRAMMING[J].Applied Mathematics A Journal of Chinese Universities,2000(2). |
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| Authors: | Lin Yixun\ Wen JianjunDeptof Math Zhengzhou Univ Zhengzhou |
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| Institution: | Lin Yixun\ Wen JianjunDept.of Math.,Zhengzhou Univ.,Zhengzhou450 0 52 . |
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| Abstract: | The basis graph \%G\% for a linear programming consists of all bases under pivot transformations. A degenerate optimal basis graph G * is a subgraph of \%G\% induced by all optimal bases at a degenerate optimal vertex x 0. In this paper, several conditions for the characterization of G * are presented. |
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| Keywords: | Linear programming degeneracy transformation graphs |
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