随机R0张量互补问题的投影Levenberg-Marquardt方法

doi:10.15960/j.cnki.issn.1007-6093.2021.04.006

Abstract

Abstract:

In this paper, we consider a class of stochastic R₀ tensor complementarity problems with finitely many elements. Firstly, we use Fischer-Burmeister function to transform the problem into a constrained optimization problem. Then a projected Levenberg-Marquardt method is used to solve the constrained optimization problem. Under general conditions, the global convergence of this method is proved, and the related numerical results show the efficiency of the method.

Key words: stochastic R₀ tensor complementarity problem, projected Levenberg-Marquardt method, global convergence, line search

CLC Number:

O221

Liyuan CUI, Shouqiang DU. Projected Levenberg-Marquardt method for stochastic R₀ tensor complementarity problems[J]. Operations Research Transactions, 2021, 25(4): 69-79.

Figures/Tables 3

References 23

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$ x^* $	$ \mathrm{val} $	$ K $
$ (0, 0.258\, 8, 0.965\, 9)^{\rm T} $	$ 4.648\, 4\times10^{-17} $	$ 7 $
$ (0, 0.258\, 8, 0.965\, 9)^{\rm T} $	$ 1.941\, 6\times10^{-17} $	$ 6 $
$ (0, 0.258\, 8, 0.965\, 9)^{\rm T} $	$ 1.320\, 9\times10^{-17} $	$ 8 $
$ (0, 0.258\, 8, 0.965\, 9)^{\rm T} $	$ 3.957\, 6\times10^{-17} $	$ 8 $
$ (0, 0.258\, 8, 0.965\, 9)^{\rm T} $	$ 5.090\, 7\times10^{-17} $	$ 7 $

$ x^* $	$ \mathrm{val} $	$ K $
$ (0.001\, 2, 1.000\, 0, 0)^{\rm T} $	$ 2.511\, 0\times10^{-13} $	$ 10 $
$ (0.000\, 8, 1.000\, 0, 0)^{\rm T} $	$ 5.670\, 8\times10^{-14} $	$ 10 $
$ (0.000\, 7, 1.000\, 0, 0)^{\rm T} $	$ 3.154\, 5\times10^{-14} $	$ 10 $
$ (0.001\, 4, 1.000\, 0, 0)^{\rm T} $	$ 4.707\, 1\times10^{-13} $	$ 11 $
$ (0.001\, 3, 1.000\, 0, 0)^{\rm T} $	$ 3.835\, 6\times10^{-13} $	$ 9 $

$ x^* $	$ \mathrm{val} $	$ K $
$ (0.710\, 8, 0.170\, 9, 0.696\, 8, 0.014\, 9)^{\rm T} $	$ 9.832\, 1\times10^{-4} $	$ 340 $
$ (0.710\, 8, 0.170\, 9, 0.696\, 8, 0.014\, 9)^{\rm T} $	$ 9.832\, 1\times10^{-4} $	$ 166 $
$ (0.710\, 8, 0.170\, 9, 0.696\, 9, 0.014\, 9)^{\rm T} $	$ 9.832\, 1\times10^{-4} $	$ 397 $
$ (0.710\, 8, 0.170\, 9, 0.696\, 9, 0.014\, 9)^{\rm T} $	$ 9.832\, 1\times10^{-4} $	$ 200 $
$ (0.710\, 8, 0.170\, 9, 0.696\, 9, 0.014\, 9)^{\rm T} $	$ 9.832\, 1\times10^{-4} $	$ 353 $

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Projected Levenberg-Marquardt method for stochastic R₀ tensor complementarity problems

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Projected Levenberg-Marquardt method for stochastic R0 tensor complementarity problems

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Projected Levenberg-Marquardt method for stochastic R₀ tensor complementarity problems