Solution of linear complementarity problems by linear programming
- 848 Downloads
The linear complementarity problem is that of finding an n x 1 vector z such that
Mz+q≧0, z≧0, zT (Mz+q)=0 where M is a given n x n real matrix and q is a given n x 1 vector. In this paper the class of matrices M for which this problem is solvable by a single linear program is enlarged to include matrices other than those that are z-matrices or those that have an inverse which is a z-matrix. (A Z-matrix is real square matrix with nonpositive offdiagonal elements.) Included in this class are other matrices such as nonnegative matrices with a strictly dominant diagonal and matrices that are the sum of a Z-matrix having a nonnegative inverse and the tensor product of any two positive vectors in Rn.
Unable to display preview. Download preview PDF.
- 2.R. W. Cottle & R. S. Sacher, “On the solution of large, structured linear complementarity problems: I,” Technical Report 73-4, Department of Operations Research, Stanford University, 1973.Google Scholar
- 3.R. W. Cottle, G. H. Golub & R. S. Sacher, “On the solution of large, structured linear complementarity problems: III,” Technical Report 74-439, Computer Science Department, Stanford University, 1974.Google Scholar
- 7.C. W. Cryer, “Free boundary problems,” forthcoming monograph.Google Scholar
- 10.O. L. Mangasarian, “Linear complementarity problems solvable by a single linear program,” University of Wisconsin Computer Sciences Technical Report #237, January 1975.Google Scholar
- 11.R. Sacher, “On the solution of large, structured linear complementarity problems: II,” Technical Report 73-5, Department of Operations Research, Stanford University, 1973.Google Scholar