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Absolute Value Equation Solution via Concave Minimization

Professor Olvi Mangasarian
UCSD Department of Mathematics


The NP-hard absolute value equation (AVE) Ax-|x|=b whereA is an n-by-n real matrix and b is an n-by-1 real vector is solved by a succession of linear programs. The linear programs arise from a reformulation of the AVE as the minimization of a piecewise-linear concave function on a polyhedral set and solving the latter bysuccessive linearization. A simple MATLAB implementationof the successive linearization algorithm solved 100 consecutivelygenerated 1000-dimensional random instances of the AVE with onlyfive violated equations out of a total of 100,000 equations.Paper is available at: ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/06-02.pdf

Tuesday, April 11, 2006
11:00AM AP&M 2402