Absolute Value Equations

Abstract

We investigate existence and nonexistence of solutions for NP-hard equations in- volving 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 so- lution for special cases. We also give nonexistence results for our AVE using theorems of the alternative and other arguments.