##### Department of Mathematics,

University of California San Diego

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### Mathematics 278 - Computational and Applied Mathematics

## Olvi Mangasarian

#### UCSD, Department of Mathematics

## Absolute value equation solution via concave minimization

##### Abstract:

The NP-hard absolute value equation (AVE), Ax-$|x|$=b, where A 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 by successive linearization. A simple MATLAB implementation of the successive linearization algorithm solved 100 consecutively generated 1000-dimensional random instances of the AVE with only five 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

Host:

### April 11, 2006

### 11:00 AM

### AP&M 7321

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