Prior Reduced Fill-In in Solving Equations in Interior Point Algorithms
Name
OR-220-90.pdf
Size
321.92 KB
Format
Adobe PDF
Checksum (MD5)
53f86120d67ebbeca269233c38d8fec4
Author(s)
Birge, John R.
Freund, Robert M.
Date Issued
July 1990
Publisher
Massachusetts Institute of Technology, Operations Research Center
Series/Report no.
Operations Research Center Working Paper;OR 220-90
Abstract
The efficiency of interior-point algorithms for linear programming is related to the effort required to factorize the matrix used to solve for the search direction at each iteration. When the linear program is in symmetric form (i.e., the constraints are Ax b, x > 0 ), then there are two mathematically equivalent forms of the search direction, involving different matrices. One form necessitates factoring a matrix whose sparsity pattern has the same form as that of (A AT). The other form necessitates factoring a matrix whose sparsity pattern has the same form as that of (ATA). Depending on the structure of the matrix A, one of these two forms may produce significantly less fill-in than the other. Furthermore, by analyzing the fill-in of both forms prior to starting the iterative phase of the algorithm, the form with the least fill-in can be computed and used throughout the algorithm. Finally, this methodology can be applied to linear programs that are not in symmetric form, that contain both equality and inequality constraints.
Subjects
interior-point algorithm, linear program, factorization, fill-in.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
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