论文信息 - An algorithm for solving the absolute value equation

An algorithm for solving the absolute value equation

Presented is an algorithm which for each A,B ∈ Rn×n and b ∈ Rn in a finite number of steps either finds a solution of the equation Ax+B|x| = b, or states existence of a singular matrix S satisfying |S − A |≤| B| (and in most cases also constructs such an S).

Jiri Rohn | J. Rohn

[1] Oleg A. Prokopyev,et al. On equivalent reformulations for absolute value equations , 2009, Comput. Optim. Appl..

[2] Olvi L. Mangasarian,et al. A generalized Newton method for absolute value equations , 2009, Optim. Lett..

[3] Olvi L. Mangasarian,et al. Absolute value equation solution via concave minimization , 2006, Optim. Lett..

[4] Olvi L. Mangasarian,et al. Absolute value programming , 2007, Comput. Optim. Appl..

[5] Wilhelm Barth,et al. Optimale Lösung von Intervallgleichungssystemen , 2005, Computing.

[6] J. Rohn. A Handbook of Results on Interval Linear Problems , 2005 .

[7] Jiri Rohn,et al. A theorem of the alternatives for the equation |Ax| − |B||x| = b , 2004, Optimization Letters.

[8] Siegfried M. Rump,et al. INTLAB - INTerval LABoratory , 1998, SCAN.

[9] Svatopluk Poljak,et al. Checking robust nonsingularity is NP-hard , 1993, Math. Control. Signals Syst..

[10] J. Rohn. Systems of linear interval equations , 1989 .

[11] Katta G. Murty,et al. Linear complementarity, linear and nonlinear programming , 1988 .

[12] J. Sherman,et al. Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix , 1950 .