On an iterative method for solving absolute value equations

We consider a class of absolute-value linear complementarity problems. We propose a new approximation reformulation of absolute value linear complementarity problems by using a nonlinear penalized equation. Based on this approximation reformulation, a penalized-equation-based generalized Newton method is proposed for solving the absolute value linear complementary problem. We show that the proposed method is globally and superlinearly convergent when the matrix of complementarity problems is positive definite and its singular values exceed 1. Numerical results show that our proposed method is very effective and efficient.

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“…. We compared our algorithm with the existing methods in [15,19]. The computational results are shown in Table 4.…”

Section: Numerical Resultsmentioning

confidence: 99%

A Penalized-Equation-Based Generalized Newton Method for Solving Absolute-Value Linear Complementarity Problems

Hai-shan

Yang

2014

Journal of Mathematics

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“…In Figure 1, we compare residual method with Noor et al 14,15 . The residual iterative method, minimization method 14 , and the iterative method 10 solve 3.1 in 51, 142, and 431 iterations, respectively.…”

Section: 4mentioning

confidence: 99%

“…We hope that this interlink among these fields may lead to discover novel and innovative techniques for solving the absolute value equations and related optimization problems. Noor et al 14,15 have suggested some iterative methods for solving absolute value equation 1.2 using minimization technique with symmetric positive definite matrix. For more details, see 3, 4, 6-12, 14-19 . In this paper, we suggest and analyse residual iterative method for solving absolute value equations 1.2 using projection technique.…”

Section: Introductionmentioning

confidence: 99%

Residual Iterative Method for Solving Absolute Value Equations

Noor

Iqbal

Al-Said

2012

Abstract and Applied Analysis

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We suggest and analyze a residual iterative method for solving absolute value equations Ax − |x| b where A ∈ R n×n , b ∈ R n are given and x ∈ R n is unknown, using the projection technique. We also discuss the convergence of the proposed method. Several examples are given to illustrate the implementation and efficiency of the method. Comparison with other methods is also given. Results proved in this paper may stimulate further research in this fascinating field.Ax − |x| b, 1.2

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“…Noor et al [9,12] have suggested and analyzed an iterative method for solving the absolute value equations using the minimization technique, in the case where the coefficient matrix is symmetric. Also Rohn [33] described an algorithm which in a finite (but exponential) number of steps computes all solutions of an absolute value equations.…”

Section: Introductionmentioning

confidence: 99%