منابع مشابه
Absolute value programming
We investigate equations, inequalities and mathematical programs involving absolute values of variables such as the equation Ax + B|x| = b, where A and B are arbitrary m × n real matrices. We show that this absolute value equation is NP-hard to solve, and that solving it solves the general linear complementarity problem. However, we propose a concave minimization problem for its solution that i...
متن کاملAbsolute Value Equations
We investigate existence and nonexistence of solutions for NP-hard equations involving absolute values of variables: Ax − |x| = b, where A is an arbitrary n × n real matrix. By utilizing an equivalence relation to the linear complementarity problem (LCP) we give existence results for this class of absolute value equations (AVEs) as well as a method of solution for special cases. We also give no...
متن کاملA uniform approximation method to solve absolute value equation
In this paper, we propose a parametric uniform approximation method to solve NP-hard absolute value equations. For this, we uniformly approximate absolute value in such a way that the nonsmooth absolute value equation can be formulated as a smooth nonlinear equation. By solving the parametric smooth nonlinear equation using Newton method, for a decreasing sequence of parameters, we can get the ...
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 کاملLinear Absolute Value Relation Analysis
Linear relation analysis (polyhedral analysis), devoted to discovering linear invariant relations among variables of a program, remains one of the most powerful abstract interpretations but is subject to convexity limitations. Absolute value enjoys piecewise linear expressiveness and thus natively fits to encode certain non-convex properties. Based on this insight, we propose to use linear abso...
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ژورنال
عنوان ژورنال: About Campus: Enriching the Student Learning Experience
سال: 2017
ISSN: 1086-4822,1536-0687
DOI: 10.1002/abc.21277