∗Received by the editors March 10, 2009. Accepted for publication August 27, 2009. Handling Editor: Daniel Szyld. †Institute of Computer Science, Czech Academy of Sciences, Prague, and School of Business Administration, Anglo-American University, Prague, Czech Republic ([email protected]). Supported by the Czech Republic Grant Agency under grants 201/09/1957 and 201/08/J020, and by the Institution...

We propose a finitely terminating primal-dual bilinear programming algorithm for the solution of the NP-hard absolute value equation (AVE): Ax− |x| = b, where A is an n× n square matrix. The algorithm, which makes no assumptions on AVE other than solvability, consists of a finite number of linear programs terminating at a solution of the AVE or at a stationary point of the bilinear program. The...

It is proved that applying sufficient regularity conditions to the interval matrix [A − |B|, A + |B|], we can create a new unique solvability condition for the absolute value equation Ax + B|x| = b, since regularity of interval matrices implies unique solvability of their corresponding absolute value equation. This condition is formulated in terms of positive definiteness of a certain point mat...

We formulate the NP-hard absolute value equation as linear complementary problem when the singular values of A exceed one, and we proposed a mixed integer linear programming method to absolute value equation problem. The effectiveness of the method is demonstrated by its ability to solve random problems.

In this article, we investigate the solution of a new class absolute value equation (NCAVE) A1x ? |B1x c| = d. Based on spectral radius condition, singular condition and row column W-property, some necessary sufficient conditions for unique solvability NCAVE are gained. Some results generalized (NGAVE) A1x?|B1x| d also obtained.