Absolute value equations

By Olvi L. Mangasarian, R. Meyer. 2006

351 citations recorded by the source corpus.

Abstract We investigate existence and nonexistence of solutions for NP-hard equations involving absolute values of variables: Ax  − ∣ x ∣ =  b , where A is an arbitrary n  ×  n real matrix. By utilizing an equivalence relation to the linear complementarity problem (LCP) we give existence results for this class of absolute value equations (AVEs) as well as a method of solution for special cases. We also give nonexistence results for our AVE using theorems of the alternative and other arguments.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/90456a66fa19a0e0593c0b52964614e1612e2698

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Q. Wei
2. Chao Zhang

In Numerical Analysis

1. Q. Wei
2. Chao Zhang

Citations in the corpus

• Global and Finite Convergence of a Generalized Newton Method for Absolute Value Equations (2009, background): “not an eigenvalue of A. By Proposition 2 of [ 4 ], the AVE (1) can be reduced to the following LCP:”