Absolute value programming

Authors:
O. L. Mangasarian
Affiliations:
Computer Sciences Department, University of Wisconsin, Madison 53706
Venue:
Computational Optimization and Applications
Year:
2007

Citing 0
Cited 7

COAP 2007 Best Paper Award

Computational Optimization and Applications
On equivalent reformulations for absolute value equations

Computational Optimization and Applications
A generalized Newton method for absolute value equations associated with second order cones

Journal of Computational and Applied Mathematics
A globally and quadratically convergent method for absolute value equations

Computational Optimization and Applications
An efficient method for optimal correcting of absolute value equations by minimal changes in the right hand side

Computers & Mathematics with Applications
Generalized symmetric accelerated over relaxation method for solving absolute value complementarity problems

Computational Mathematics and Mathematical Physics
Equilibrium problems involving the Lorentz cone

Journal of Global Optimization

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Abstract

We investigate equations, inequalities and mathematical programs involving absolute values of variables such as the equation Ax+B|x| = b, where A and B are arbitrary m脳 n real matrices. We show that this absolute value equation is NP-hard 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.