Quasi-Newton Method for Absolute Value Equation Based on Upper Uniform Smoothing Approximation - Longquan Yong; Shouheng Tuo (TELKOMNIKA (Telecommunication Computing Electronics and Control), 2016)
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, absolute value equation (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 given AVE problems demonstrated that our algorithm is valid and superior to lower uniform smooth approximation function.