By utilizing a dual complementarity property, we propose a new linear programming method for solving the NP-hard absolute value equation (AVE): Ax−|x| = b, where A is an n×n square matrix. The algorithm makes no assumptions on the AVE other than solvability and consists of solving a few linear programs, typically less than four. The algorithm was tested on 500 consecutively generated random sol...

The NP-hard absolute value equation (AVE) Ax − |x| = b where A ∈ R and b ∈ Rn is solved by a succession of linear programs. The linear programs arise from a reformulation of the AVE as the minimization of a piecewise-linear concave function on a polyhedral set and solving the latter by successive linearization. A simple MATLAB implementation of the successive linearization algorithm solved 100 ...

In this paper, we present a new approach for solving absolute value equation (AVE) whichuse Levenberg-Marquardt method with conjugate subgradient structure. In conjugate subgradientmethods the new direction obtain by combining steepest descent direction and the previous di-rection which may not lead to good numerical results. Therefore, we replace the steepest descentdir...

Abstract The p -adic completion ? of the rational numbers induces a different absolute value |?| than typical | ?| we have on real numbers. In this paper compare and contrast functions f : ? + ? , for which composition with p-adic metric d generated by is still usual preserving that preserve Euclidean ?. particular, it shown ? an ultrametric if only there function g such = every . Some general ...