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数学进展 - 2020, Vol. 49(6): 761-768
A Smoothing Newton Method for Tensor Generalized Absolute Value Equations

郭旭, 谷伟哲
GUO Xu, GU Weizhe*

天津大学数学学院, 天津, 300350
School of Mathematics, Tianjin University, Tianjin, 300350, P. R. China

收稿日期: 2019-07-23
出版日期: 2020-11-17
2020, Vol. 49(6): 761-768
DOI: 10.11845/sxjz.2019084b

[187 KB]

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摘要 本文提出了一种求解广义张量绝对值方程的光滑化牛顿算法. 广义张量绝对值方程是对矩阵广义绝对值方程的推广, 目前得到了广泛的关注. 我们证明了在一种弱且容易验证的条件下, 光滑牛顿算法是有全局收敛性的, 同时我们给出了数值实验来说明算法的有效性.
关键词 张量绝对值方程光滑牛顿算法强$P_{0}$张量    
Abstract:In this paper, we propose a smoothing Newton method to solve the tensor generalized absolute value equations (TGAVEs). TGAVEs are a generalization of matrix generalized absolute value equations (GAVEs) and nowadays have attracted a lot of attention. Under a weak and easily checkable condition, the smoothing Newton method is proved to be globally convergent. We also give some numerical results, which show that the algorithm is efficient.
Key wordstensor absolute value equation    smooth Newton method    strong $P_{0}$ tensor
PACS:  O224  
[1] Bai X.L., Huang Z.H. and Wang Y., Global uniqueness and solvability for tensor complementarity
problems, J. Optim. Theory Appl., 2016, 170(1): 72-84.
[2] Caccetta L., Qu B. and Zhou G.L., A globally and quadratically convergent method for absolute value equations, Comput. Optim. Appl., 2011, 48(1): 45-58.
[3] Du S.Q., Zhang L.P., Chen C.Y. and Qi L.Q., Tensor absolute value equations, Sci. China Math., 2018, 61(9): 1695-1710.
[4] Han J.Y., Xiu N.H. and Qi H.D., Nonlinear Complementarity Theory and Algorithm, Shanghai: Science and Technology Press, 2006 (in Chinese).
[5] Hu S.L., Huang Z.H. and Zhang Q., A generalized Newton method for absolute value equations associated with second order cones, [J]. Comput. Appl. Math., 2011, 235(5): 1490-1501.
[6] Huang Z.H., Zhang Y. and Wu W., A smoothing-type algorithm for solving system of inequalities, [J]. Comput. Appl. Math., 2008, 220(1/2): 355-363.
[7] Jiang X.Q.,A smoothing Newton method for solving absolute value equations, Adv. Mater. Res., 2013, (765/766/767): 703-708.
[8] Jiang, X.Q. and Zhang, Y., A smoothing-type algorithm for absolute value equations, [J]. Ind. Manag. Optim., 2013, 9(4): 789-798.
[9] Ling C., Yan W.J., He H.J. and Qi L.Q., Further study on tensor absolute value equations, Sci. China Math., 2020, 63(10): 2137-2156.
[10] Mangasarian O.L.,Absolute value programming, Comput. Optim. Appl., 2007, 36(1): 43-53.
[11] Mangasarian, O.L. and Meyer, R.R., Absolute value equations, Linear Algebra Appl., 2006, 419(2): 359-367.
[12] Miao X., Yang J., Saheya B. and Chen J.S., A smoothing Newton method for absolute value equation associated with second-order cone, Appl. Numer. Math., 2017, 120: 82-96.
[13] Prokopyev O.A.,On equivalent reformulations for absolute value equations, Comput. Optim. Appl., 2009, 44(3): 363-372.
[14] Prokopyev O.A., Butenko S. and Trapp A., Checking solvability of systems of interval linear equations and inequalities via mixed integer programming, European [J]. Oper. Res., 2009, 199(1): 117-121.
[15] Rohn J.,A theorem of the alternatives for the equation Ax+B|x|=b, Optim. Lett., 2012, 6(3): 585-591.
[16] Sun D.,A regularization Newton method for solving nonlinear complementarity problems, Appl. Math. Optim., 1999, 40(3): 315-339.
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