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A modified smoothing and regularized Newton method for monotone second-order cone complementarity problems

机译:单调二阶锥互补问题的改进的平滑正则牛顿方法

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In this paper, we propose a globally and quadratically convergent Newton-type algorithm for solving monotone second-order cone complementarity problems (denoted by SOCCPs). This algorithm is based on smoothing and regularization techniques by incorporating smoothing Newton's method. Many Newton-type methods with smoothing and regularization techniques have been studied for solving nonlinear complementarity problems (NCPs) and box constrained variational inequalities (BVIs). Our algorithm is regarded as an extension of those methods to SOCCP. However, it is different from the existing methods, because we solve SOCCP by treating both the smoothing parameter μ and the regularization parameter ε as independent variables. In addition, numerical experiments indicate that the proposed method is quite effective.
机译:在本文中,我们提出了一种全局和二次收敛的牛顿型算法,用于求解单调二阶锥互补问题(以SOCCP表示)。该算法基于平滑和正则化技术,并结合了平滑牛顿法。为了解决非线性互补问题(NCP)和盒约束变分不等式(BVI),已经研究了许多采用平滑和正则化技术的牛顿型方法。我们的算法被认为是这些方法对SOCCP的扩展。但是,它与现有方法不同,因为我们通过将平滑参数μ和正则化参数ε视为自变量来求解SOCCP。另外,数值实验表明该方法是有效的。

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