Discrete Potential Optimization for Absolute Value Equations: A Sign-Flip Framework with Polynomial Complexity

Solving the AVE $Ax - |x| = b$ is generally NP-hard. Existing approaches mostly operate in continuous variable spaces, with the notable exception of Rohn's sign-accord algorithm, which incurs an exponential worst-case bound of $2^n$ iterations. To overcome this bottleneck, we develop a discrete pote