Computational Optimization and Applications
, Volume 36, Issue 1, pp 4353
First online:
Absolute value programming
 O. L. MangasarianAffiliated withComputer Sciences Department, University of Wisconsin Email author
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We investigate equations, inequalities and mathematical programs involving absolute values of variables such as the equation Ax+Bx = b, where A and B are arbitrary m× n real matrices. We show that this absolute value equation is NPhard to solve, and that solving it with B = I solves the general linear complementarity problem. We give sufficient optimality conditions and duality results for absolute value programs as well as theorems of the alternative for absolute value inequalities. We also propose concave minimization formulations for absolute value equations that are solved by a finite succession of linear programs. These algorithms terminate at a local minimum that solves the absolute value equation in almost all solvable random problems tried.
Keywords
Absolute value (AV) equations AV algorithm AV theorems of alternative AV duality Title
 Absolute value programming
 Journal

Computational Optimization and Applications
Volume 36, Issue 1 , pp 4353
 Cover Date
 200701
 DOI
 10.1007/s1058900603955
 Print ISSN
 09266003
 Online ISSN
 15732894
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Absolute value (AV) equations
 AV algorithm
 AV theorems of alternative
 AV duality
 Industry Sectors
 Authors

 O. L. Mangasarian ^{(1)}
 Author Affiliations

 1. Computer Sciences Department, University of Wisconsin, Madison, WI, 53706