#### Efficient signed backward substitution for piecewise affine functions via path problems in a directed acyclic graph

We introduce an efficient signed backward substitution for a highly-structured system. More precisely, the problem is to find a vector u of dimension s that solves the system of piecewise affine equations u = c + L|u|, where L is a strictly lower left triangular s times s matrix, c denotes a given vector of dimension s, and the notation |cdot| indicates the component-wise absolute value of a vector. The novel approach is based on a Neumann series reformulation and attempts to exploit a high ... Read more