期刊名称：TELKOMNIKA (Telecommunication Computing Electronics and Control)
印刷版ISSN：2302-9293
出版年度：2016
卷号：14
期号：3
页码：1134-1141
DOI：10.12928/telkomnika.v14i3.3785
语种：English
出版社：Universitas Ahmad Dahlan
摘要：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.
其他摘要：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.
