THE P-MATRIX PROBLEM IS CO-NP-COMPLETE

被引：50
|
作者：
COXSON, GE
机构：
[1] Department of Electrical and Computer Engineering, University of Wisconsin-Madison, Madison, 53705, WI
来源：
MATHEMATICAL PROGRAMMING | 1994年 / 64卷 / 02期
关键词：
P-MATRIX; LINEAR COMPLEMENTARITY PROBLEM; INTERVAL MATRIX; NP-COMPLETE;
D O I：
10.1007/BF01582570
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
Recently Rohn and Poljak proved that for interval matrices with rank-one radius matrices testing singularitY is NP-complete. This paper will show that given any matrix family belonging to the class of matrix polytopes with hypercube domains and rank-one perturbation matrices, a class which contains the interval matrices, testing singularity reduces to testing whether a certain matrix is not a P-matrix. It follows from this result that the problem of testing whether a given matrix is a P-matrix is co-NP-complete.
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页码：173 / 178
页数：6
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