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- W2153923003 abstract "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. Index Terms—absolute value equation; linear complementary problem; mixed integer linear programming. The basic contribution of the present work is a simple algorithm based on a new reformulation of the AVE (1) as a mixed integer linear programming minimization problem. We prove that the solution to mixed integer linear programming is existent. This turns out to be an effective way for solving the AVE as indicated by computational results on some random AVEs. In Sect. 2 of the present work we transform AVE into linear complementary problem when the singular values of A exceed 1. We solve linear complementary problem by mixed integer linear programming method in Sect. 3, and we prove that the solution to mixed integer linear programming is existent under certain assumptions. Effectiveness of the method is demonstrated in Sect. 4 by solving some randomly generated AVEs problem with singular values of A exceeding 1. Section 5 concludes the paper. Section 6 is acknowledgement." @default.
- W2153923003 created "2016-06-24" @default.
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- W2153923003 date "2009-01-01" @default.
- W2153923003 modified "2023-09-27" @default.
- W2153923003 title "Mixed Integer Linear Programming Method for Absolute Value Equations" @default.
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