A Nonmonotone Smoothing Newton Algorithm for Weighted Complementarity Problem

Tang, Jingyong; Zhang, Hongchao

doi:10.1007/s10957-021-01839-6

Cited by 18 publications

(13 citation statements)

References 33 publications

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“…We should mention that the equation (3.15) plays the key role in the proof of Theorem 3.1. This equation motivates us to develop the algorithm with the property β (k) < µ (k) , which is slightly different from that given in [39] (β (k) ≤ µ (k) was proved there).…”

Section: The Non-monotone Smoothing Newton Algorithm For Gave (11)mentioning

confidence: 91%

“…Remark 3.1. The development of Algorithm 1 is inspired by the non-monotone smoothing Newton algorithm for the weighted complementarity problem [39] and the non-monotone Levenberg-Marquardt type method for the weighted nonlinear complementarity problem [41].…”

Section: The Non-monotone Smoothing Newton Algorithm For Gave (11)mentioning

confidence: 99%

“…However, monotone line search techniques were used in the methods proposed in [29,40]. Recently, great attention has been paid to smoothing algorithms with nonmonotone line search; see, e.g., [16,38,39,52] and references therein. Non-monotone line search schemes can improve the likelihood of finding a global optimum and improve convergence speed in cases where a monotone line search scheme is forced to creep along the bottom of a narrow curved valley [50].…”

Section: Introductionmentioning

confidence: 99%

“…This motivates us to develop a non-monotone smoothing Newton algorithm for solving GAVE (1.1). Our work here is inspired by recent studies on weighted complementarity problem [39,41].…”

Section: Introductionmentioning

confidence: 99%

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A non-monotone smoothing Newton algorithm for solving the system of generalized absolute value equations

Chen

Yu²,

Han

et al. 2021

Preprint

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The system of generalized absolute value equations (GAVE) has attracted more and more attention in the optimization community. In this paper, by introducing a smoothing function, we develop a smoothing Newton algorithm with non-monotone line search to solve the GAVE. We show that the non-monotone algorithm is globally and locally quadratically convergent under a weaker assumption than those given in most existing algorithms for solving the GAVE. Numerical results are given to demonstrate the viability and efficiency of the approach.

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Section: The Non-monotone Smoothing Newton Algorithm For Gave (11)mentioning

confidence: 91%

Section: The Non-monotone Smoothing Newton Algorithm For Gave (11)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…This motivates us to develop a non-monotone smoothing Newton algorithm for solving GAVE (1.1). Our work here is inspired by recent studies on weighted complementarity problem [39,41].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A non-monotone smoothing Newton algorithm for solving the system of generalized absolute value equations

Chen

Yu²,

Han

et al. 2021

Preprint

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“…Equation ( 19) is the iterative formula of Newton algorithm [34,35]. Still, the algorithm has strict requirements on the function, and the computational complexity is high because the optimization direction does not necessarily decrease towards the direction of the function value.…”

Section: Ellipsoid Fitting Based On Lm-rlsmentioning

confidence: 99%

Improved ellipsoid fitting aided geomagnetic sensor calibration algorithm

Jiang,

Tan

2024

Meas. Sci. Technol.

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Aiming at the problems that the traditional single ellipsoid fitting fails to eliminate the errors of the geomagnetic sensor and does not consider the geomagnetic anomaly information, etc., this paper proposes a Robust Least Squares combined with the Levenberg-Marquardt (LM-RLS) algorithm to fit an accurate ellipsoid to achieve accurate data calibration. According to the geomagnetic sensor error model, the total amount of geomagnetism is used as the constraint, the fitted ellipsoid coefficients of Robust Least Squares (RLS) are used as the initial values, and the LM algorithm is used to calculate the magnetic field dispersion points to the nearest point of the fitted ellipsoid surface. Then, the initial calibration value is solved by the criterion of the minimum weighted sum of squares of the closest point distance. Finally, the accurate ellipsoid is obtained to realize data calibration. The results of the dynamic experiment show that after the ellipsoid is precisely fitted by the LM-RLS algorithm, the sum of the absolute values of the distance from the magnetic field discrete data to the ellipsoid surface is reduced by 48.33% (RLS) and 43.10% (RWTLS). The relative errors of the magnetic field in the X, Y, and Z axes are reduced from 0.48%, 0.78%, 1.48% (RLS) and 0.30%, 0.58%, 1.14% (RWTLS) to 0.10%, 0.04%, 0.16 %, respectively. The accuracy of geomagnetic calibration is improved by 68.06% (RLS) and 61.02% (RWTLS) in the dynamic experiment. The algorithm improves the accuracy of geomagnetic measurement, which provides a new idea for the calibration of three-axis geomagnetic sensors.

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