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Статті в журналах з теми "Smoothing Newton method"

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Автор: Grafiati

Опубліковано: 18 січня 2023

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1

Zhu, Jianguang, and Binbin Hao. "A new smoothing method for solving nonlinear complementarity problems." Open Mathematics 17, no. 1 (March 10, 2019): 104–19. http://dx.doi.org/10.1515/math-2019-0011.

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Abstract In this paper, a new improved smoothing Newton algorithm for the nonlinear complementarity problem was proposed. This method has two-fold advantages. First, compared with the classical smoothing Newton method, our proposed method needn’t nonsingular of the smoothing approximation function; second, the method also inherits the advantage of the classical smoothing Newton method, it only needs to solve one linear system of equations at each iteration. Without the need of strict complementarity conditions and the assumption of P0 property, we get the global and local quadratic convergence properties of the proposed method. Numerical experiments show that the efficiency of the proposed method.

2

WU, CAIYING, and GUOQING CHEN. "PREDICTOR–CORRECTOR SMOOTHING NEWTON METHOD FOR SOLVING SEMIDEFINITE PROGRAMMING." Bulletin of the Australian Mathematical Society 79, no. 3 (April 17, 2009): 367–76. http://dx.doi.org/10.1017/s0004972708001214.

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AbstractThere has been much interest recently in smoothing methods for solving semidefinite programming (SDP). In this paper, based on the equivalent transformation for the optimality conditions of SDP, we present a predictor–corrector smoothing Newton algorithm for SDP. Issues such as the existence of Newton directions, boundedness of iterates, global convergence, and local superlinear convergence of our algorithm are studied under suitable assumptions.

3

Feng, Ning, Zhi Yuan Tian, and Xin Lei Qu. "A Smoothing Newton Method for Nonlinear Complementarity Problems." Applied Mechanics and Materials 475-476 (December 2013): 1090–93. http://dx.doi.org/10.4028/www.scientific.net/amm.475-476.1090.

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A new FB-function based on the P0 function is given in this paper. The nonlinear complementarity problem is reformulated to solve equivalent equations based on the FB-function. A modified smooth Newton method is proposed for nonlinear complementarity problem. Under mild conditions, the global convergence of the algorithm is proved. The numerical experiment shows that the algorithm is potentially efficient.

4

Yong, Longquan. "A Smoothing Newton Method for Absolute Value Equation." International Journal of Control and Automation 9, no. 2 (February 28, 2016): 119–32. http://dx.doi.org/10.14257/ijca.2016.9.2.12.

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5

Li, Dong-Hui, Liqun Qi, Judy Tam, and Soon-Yi Wu. "A Smoothing Newton Method for Semi-Infinite Programming." Journal of Global Optimization 30, no. 2-3 (November 2004): 169–94. http://dx.doi.org/10.1007/s10898-004-8266-z.

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6

Tang, Jingyong, Li Dong, Jinchuan Zhou, and Liang Fang. "A smoothing Newton method for nonlinear complementarity problems." Computational and Applied Mathematics 32, no. 1 (March 26, 2013): 107–18. http://dx.doi.org/10.1007/s40314-013-0015-9.

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7

Li, Meixia, and Haitao Che. "A Smoothing Inexact Newton Method for Generalized Nonlinear Complementarity Problem." Mathematical Problems in Engineering 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/401835.

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Based on the smoothing function of penalized Fischer-Burmeister NCP-function, we propose a new smoothing inexact Newton algorithm with non-monotone line search for solving the generalized nonlinear complementarity problem. We view the smoothing parameter as an independent variable. Under suitable conditions, we show that any accumulation point of the generated sequence is a solution of the generalized nonlinear complementarity problem. We also establish the local superlinear (quadratic) convergence of the proposed algorithm under the BD-regular assumption. Preliminary numerical experiments indicate the feasibility and efficiency of the proposed algorithm.

8

Qi, L., and D. Sun. "Smoothing Functions and Smoothing Newton Method for Complementarity and Variational Inequality Problems." Journal of Optimization Theory and Applications 113, no. 1 (April 2002): 121–47. http://dx.doi.org/10.1023/a:1014861331301.

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9

Yin, Hongxia. "An Adaptive Smoothing Method for Continuous Minimax Problems." Asia-Pacific Journal of Operational Research 32, no. 01 (February 2015): 1540001. http://dx.doi.org/10.1142/s0217595915400011.

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Анотація:

A simple and implementable two-loop smoothing method for semi-infinite minimax problem is given with the discretization parameter and the smoothing parameter being updated adaptively. We prove the global convergence of the algorithm when the steepest descent method or a BFGS type quasi-Newton method is applied to the smooth subproblems. The strategy for updating the smoothing parameter can not only guarantee the convergence of the algorithm but also considerably reduce the ill-conditioning caused by increasing the value of the smoothing parameter. Numerical tests show that the algorithm is robust and effective.

10

Meng, Wei, Zhi Yuan Tian, and Xin Lei Qu. "A Smoothing Method for Solving the NCP Based on a New Smoothing Approximate Function." Applied Mechanics and Materials 462-463 (November 2013): 294–97. http://dx.doi.org/10.4028/www.scientific.net/amm.462-463.294.

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Анотація:

A new smoothing approximate function of the FischerBurmeister function is given. A modified smoothing Newton method based on the function is proposed for solving a kind of nonlinear complementarity problems. Under suitable conditions, the global convergence of the method is proved. Numerical results show the effectiveness of the method.

11

Zheng, Xiuyun, and Jiarong Shi. "Smoothing Newton method for generalized complementarity problems based on a new smoothing function." Applied Mathematics and Computation 231 (March 2014): 160–68. http://dx.doi.org/10.1016/j.amc.2013.12.170.

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12

Dong, Li, Bo Yu, and Yu Xiao. "A Spline Smoothing Newton Method for Semi-Infinite Minimax Problems." Journal of Applied Mathematics 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/852074.

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Based on discretization methods for solving semi-infinite programming problems, this paper presents a spline smoothing Newton method for semi-infinite minimax problems. The spline smoothing technique uses a smooth cubic spline instead of max function and only few components in the max function are computed; that is, it introduces an active set technique, so it is more efficient for solving large-scale minimax problems arising from the discretization of semi-infinite minimax problems. Numerical tests show that the new method is very efficient.

13

Mavriplis, Dimitri J. "A residual smoothing strategy for accelerating Newton method continuation." Computers & Fluids 220 (April 2021): 104859. http://dx.doi.org/10.1016/j.compfluid.2021.104859.

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14

Jiang, Xiao Qin. "A Smoothing Newton Method for Solving Absolute Value Equations." Advanced Materials Research 765-767 (September 2013): 703–8. http://dx.doi.org/10.4028/www.scientific.net/amr.765-767.703.

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Анотація:

In this paper, we reformulate the system of absolute value equations as afamily of parameterized smooth equations and propose a smoothing Newton method tosolve this class of problems. we prove that the method is globally and locally quadraticallyconvergent under suitable assumptions. The preliminary numerical results demonstratethat the method is effective.

15

Zheng, Xiuyun, and Hongwei Liu. "A smoothing inexact Newton method for variational inequality problems." International Journal of Computer Mathematics 88, no. 6 (April 2011): 1283–93. http://dx.doi.org/10.1080/00207160.2010.500663.

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16

Chi, Xiaoni, Zhongping Wan, Zhibin Zhu, and Liuyang Yuan. "A nonmonotone smoothing Newton method for circular cone programming." Optimization 65, no. 12 (August 7, 2016): 2227–50. http://dx.doi.org/10.1080/02331934.2016.1217861.

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17

Wan, Zhong, HuanHuan Li, and Shuai Huang. "A Smoothing Inexact Newton Method for Nonlinear Complementarity Problems." Abstract and Applied Analysis 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/731026.

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A smoothing inexact Newton method is presented for solving nonlinear complementarity problems. Different from the existing exact methods, the associated subproblems are not necessary to be exactly solved to obtain the search directions. Under suitable assumptions, global convergence and superlinear convergence are established for the developed inexact algorithm, which are extensions of the exact case. On the one hand, results of numerical experiments indicate that our algorithm is effective for the benchmark test problems available in the literature. On the other hand, suitable choice of inexact parameters can improve the numerical performance of the developed algorithm.

18

Xiu, Naihua, and Jianzhong Zhang. "A smoothing Gauss–Newton method for the generalized HLCP." Journal of Computational and Applied Mathematics 129, no. 1-2 (April 2001): 195–208. http://dx.doi.org/10.1016/s0377-0427(00)00550-1.

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19

Rui, Shao-Ping, and Cheng-Xian Xu. "A smoothing inexact Newton method for nonlinear complementarity problems." Journal of Computational and Applied Mathematics 233, no. 9 (March 2010): 2332–38. http://dx.doi.org/10.1016/j.cam.2009.10.018.

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20

吴, 振. "A Uniformly Smoothing Newton Method for Support Vector Machine." Operations Research and Fuzziology 10, no. 01 (2020): 86–99. http://dx.doi.org/10.12677/orf.2020.101010.

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21

Liu, Jing, and Yan Gao. "Smoothing Newton method for operator equations in Banach spaces." Journal of Applied Mathematics and Computing 28, no. 1-2 (June 17, 2008): 447–60. http://dx.doi.org/10.1007/s12190-008-0118-4.

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22

Liu, Lixia, Sanyang Liu, and Yan Wu. "A smoothing Newton method for symmetric cone complementarity problem." Journal of Applied Mathematics and Computing 47, no. 1-2 (March 25, 2014): 175–91. http://dx.doi.org/10.1007/s12190-014-0768-3.

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23

Tang, Jia, and Changfeng Ma. "A smoothing Newton method for symmetric cone complementarity problems." Optimization Letters 9, no. 2 (November 7, 2013): 225–44. http://dx.doi.org/10.1007/s11590-013-0704-8.

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24

Dong, Li, and Bo Yu. "A spline smoothing Newton method for finite minimax problems." Journal of Engineering Mathematics 93, no. 1 (December 13, 2014): 145–58. http://dx.doi.org/10.1007/s10665-014-9733-2.

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25

Xiao, Yu, and Bo Yu. "A truncated aggregate smoothing Newton method for minimax problems." Applied Mathematics and Computation 216, no. 6 (May 2010): 1868–79. http://dx.doi.org/10.1016/j.amc.2009.11.034.

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26

Rapajić, Sanja, and Zoltan Papp. "A nonmonotone Jacobian smoothing inexact Newton method for NCP." Computational Optimization and Applications 66, no. 3 (October 11, 2016): 507–32. http://dx.doi.org/10.1007/s10589-016-9881-6.

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27

Xu, H. "Adaptive Smoothing Method, Deterministically Computable Generalized Jacobians, and the Newton Method." Journal of Optimization Theory and Applications 109, no. 1 (April 2001): 215–24. http://dx.doi.org/10.1023/a:1017526207997.

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28

Zhu, Jianguang, and Binbin Hao. "A SMOOTHING NEWTON METHOD FOR NCP BASED ON A NEW CLASS OF SMOOTHING FUNCTIONS." Journal of applied mathematics & informatics 32, no. 1_2 (January 30, 2014): 211–25. http://dx.doi.org/10.14317/jami.2014.211.

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29

Zhang, Jian, and Ke-Cun Zhang. "A variant smoothing Newton method for P0-NCP based on a new smoothing function." Journal of Computational and Applied Mathematics 225, no. 1 (March 2009): 1–8. http://dx.doi.org/10.1016/j.cam.2008.06.012.

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30

Zhu, Jianguang, and Binbin Hao. "A new class of smoothing functions and a smoothing Newton method for complementarity problems." Optimization Letters 7, no. 3 (January 4, 2012): 481–97. http://dx.doi.org/10.1007/s11590-011-0432-x.

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31

董, 丽. "Smoothing Inexact Newton Method for the Second Order Cone Programming." Advances in Applied Mathematics 04, no. 03 (2015): 271–76. http://dx.doi.org/10.12677/aam.2015.43033.

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32

Chen, Xiaohong, and Changfeng Ma. "A regularization smoothing Newton method for solving nonlinear complementarity problem." Nonlinear Analysis: Real World Applications 10, no. 3 (June 2009): 1702–11. http://dx.doi.org/10.1016/j.nonrwa.2008.02.010.

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33

Yu, Zhensheng, and Yi Qin. "A cosh-based smoothing Newton method for nonlinear complementarity problem." Nonlinear Analysis: Real World Applications 12, no. 2 (April 2011): 875–84. http://dx.doi.org/10.1016/j.nonrwa.2010.08.012.

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34

Kong, Lingchen, Jie Sun, and Naihua Xiu. "A Regularized Smoothing Newton Method for Symmetric Cone Complementarity Problems." SIAM Journal on Optimization 19, no. 3 (January 2008): 1028–47. http://dx.doi.org/10.1137/060676775.

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35

Pan, S. H., and Y. X. Jiang. "Smoothing Newton Method for Minimizing the Sum of p-Norms." Journal of Optimization Theory and Applications 137, no. 2 (April 12, 2008): 255–75. http://dx.doi.org/10.1007/s10957-008-9364-8.

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36

Zhang, Xinzhen, Hefeng Jiang, and Yiju Wang. "A smoothing Newton-type method for generalized nonlinear complementarity problem." Journal of Computational and Applied Mathematics 212, no. 1 (February 2008): 75–85. http://dx.doi.org/10.1016/j.cam.2006.03.042.

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37

Buhmiler, Sandra, and Nataša Krejić. "A new smoothing quasi-Newton method for nonlinear complementarity problems." Journal of Computational and Applied Mathematics 211, no. 2 (February 2008): 141–55. http://dx.doi.org/10.1016/j.cam.2006.11.007.

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38

Qi, Hou-Duo, and Li-Zhi Liao. "A Smoothing Newton Method for Extended Vertical Linear Complementarity Problems." SIAM Journal on Matrix Analysis and Applications 21, no. 1 (January 1999): 45–66. http://dx.doi.org/10.1137/s0895479897329837.

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39

Xie, Weisong, and Caiying Wu. "Smoothing inexact Newton method for solving P 0-NCP problems." Transactions of Tianjin University 19, no. 5 (October 2013): 385–90. http://dx.doi.org/10.1007/s12209-013-1909-8.

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40

Li, Yuan Min, Xing Tao Wang, and De Yun Wei. "A smoothing Newton method for NCPs with the P0-property." Applied Mathematics and Computation 217, no. 16 (April 2011): 6917–25. http://dx.doi.org/10.1016/j.amc.2011.01.099.

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41

Yang, Liu, Yanping Chen, Xiaojiao Tong, and Chunlin Deng. "A new smoothing Newton method for solving constrained nonlinear equations." Applied Mathematics and Computation 217, no. 24 (August 2011): 9855–63. http://dx.doi.org/10.1016/j.amc.2011.04.045.

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42

Liu, Ruijuan, and Li Dong. "Nonmonotone smoothing inexact Newton method for the nonlinear complementarity problem." Journal of Applied Mathematics and Computing 51, no. 1-2 (August 29, 2015): 659–74. http://dx.doi.org/10.1007/s12190-015-0925-3.

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43

Feng, Ye, Liu Hongwei, Zhou Shuisheng, and Liu Sanyang. "A smoothing trust-region Newton-CG method for minimax problem." Applied Mathematics and Computation 199, no. 2 (June 2008): 581–89. http://dx.doi.org/10.1016/j.amc.2007.10.070.

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44

Ma, Changfeng. "A new smoothing quasi-Newton method for nonlinear complementarity problems." Applied Mathematics and Computation 171, no. 2 (December 2005): 807–23. http://dx.doi.org/10.1016/j.amc.2005.01.088.

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45

Rapajić, Sanja, Nataša Krejić, and Zorana Lužanin. "On a Smoothing Quasi-Newton Method for Nonlinear Complementarity Problems." PAMM 3, no. 1 (December 2003): 523–24. http://dx.doi.org/10.1002/pamm.200310531.

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46

Tang, Jingyong, Guoping He, Li Dong, and Liang Fang. "A smoothing Newton method for second-order cone optimization based on a new smoothing function." Applied Mathematics and Computation 218, no. 4 (October 2011): 1317–29. http://dx.doi.org/10.1016/j.amc.2011.06.015.

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47

Huang, Na, and Changfeng Ma. "A regularized smoothing Newton method for solving SOCCPs based on a new smoothing C-function." Applied Mathematics and Computation 230 (March 2014): 315–29. http://dx.doi.org/10.1016/j.amc.2013.12.116.

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48

Liu, Lixia, and Sanyang Liu. "A smoothing Newton method based on a one-parametric class of smoothing function for SOCCP." Journal of Applied Mathematics and Computing 36, no. 1-2 (June 11, 2010): 473–87. http://dx.doi.org/10.1007/s12190-010-0414-7.

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49

Arenas, Favian E., Héctor Jairo Martínez, and Rosana Pérez. "A local Jacobian smoothing method for solving Nonlinear Complementarity Problems." Universitas Scientiarum 25, no. 1 (May 4, 2020): 149–74. http://dx.doi.org/10.11144/javeriana.sc25-1.aljs.

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Анотація:

In this paper, we present a smoothing of a family of nonlinear complementarity functions and use its properties in combination with the smooth Jacobian strategy to present a new generalized Newton-type algorithm to solve a nonsmooth system of equations equivalent to the Nonlinear Complementarity Problem. In addition, we prove that the algorithm converges locally and q-quadratically, and analyze its numerical performance.

50

Zeng, You Fang, Jin Bao Jian, and Chun Ming Tang. "A New Smoothing Method Based on Nonsmooth FB Function for Second-Order Cone Programming." Advanced Materials Research 532-533 (June 2012): 1000–1005. http://dx.doi.org/10.4028/www.scientific.net/amr.532-533.1000.

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Анотація:

Based on a new smoothing function of the well-known nonsmooth FB (Fischer-Burmeis-ter) function, a smoothing Newton-type method for second-order cone programming problems is presented in this paper. The features of this method are following: firstly, the starting point can be chosen arbitrarily; secondly, at each iteration, only one system of linear equations and one line search are performed; finally, global, strong convergence and Q-quadratic convergent rate are obtained. The numerical results demonstrate the effectiveness of the algorithm.