Quasi-Newton Method for Absolute Value Equation Based on Upper Uniform Smoothing Approximation Function
Abstract: Generally, absolute
value equation (AVE), Ax - |x| = b, is an NP-hard problem. Especially, how to find
all solutions of AVE with multi-solutions is actually a more difficult problem.
In this paper, an upper uniform smooth approximation function of absolute value
function is proposed, and some properties of uniform smooth approximation
function are studied. Then, AVE, Ax - |x| = b, where A is a square matrix whose
singular values exceed one, is transformed into smooth optimization problem by
using the upper uniform smooth approximation function, and solved by
quasi-Newton method. Numerical results in solving some given AVE problems
demonstrated that our algorithm is valid and superior to that by lower uniform smooth
approximation function.
Keywords: quasi-Newton method,
absolute value equation, absolute value function, upper uniform smoothing
approximation function, singular value
Author: Longquan Yong,
Shouheng Tuo
Journal Code: jptkomputergg160158
