The proximal methods for solving absolute value equation
نویسندگان
چکیده
منابع مشابه
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).
متن کاملA hybrid algorithm for solving the absolute value equation
We propose a hybrid algorithm for solving the NP-hard absolute value equation (AVE): Ax−|x| = b, where A is an n×n square matrix. The algorithm makes no assumptions on the AVE other than solvability and consists of solving iteratively a linear system of equations followed by a linear program. The algorithm was tested on 100 consecutively generated random solvable instances of the AVE with n =50...
متن کاملEla an Algorithm for Solving the Absolute Value Equation∗
∗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...
متن کاملAugmented Lagrangian method for solving absolute value equation and its application in two-point boundary value problems
One of the most important topic that consider in recent years by researcher is absolute value equation (AVE). The absolute value equation seems to be a useful tool in optimization since it subsumes the linear complementarity problem and thus also linear programming and convex quadratic programming. This paper introduce a new method for solving absolute value equation. To do this, we transform a...
متن کاملA note on unique solvability of the absolute value equation
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 deniteness of a certain point matrix...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Numerical Algebra, Control & Optimization
سال: 2021
ISSN: 2155-3297
DOI: 10.3934/naco.2020037