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Journal articles on the topic 'Semismooth'

Author: Grafiati

Published: 24 April 2022

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1

Sun, Defeng, and Jie Sun. "Semismooth Matrix-Valued Functions." Mathematics of Operations Research 27, no. 1 (February 2002): 150–69. http://dx.doi.org/10.1287/moor.27.1.150.342.

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2

Farrell, Patrick E., Matteo Croci, and Thomas M. Surowiec. "Deflation for semismooth equations." Optimization Methods and Software 35, no. 6 (May 16, 2019): 1248–71. http://dx.doi.org/10.1080/10556788.2019.1613655.

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3

Bolte, Jérôme, Aris Daniilidis, and Adrian Lewis. "Tame functions are semismooth." Mathematical Programming 117, no. 1-2 (July 21, 2007): 5–19. http://dx.doi.org/10.1007/s10107-007-0166-9.

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4

Yang, Y. F. "A new trust region method for nonsmooth equations." ANZIAM Journal 44, no. 4 (April 2003): 595–607. http://dx.doi.org/10.1017/s1446181100012967.

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AbstractWe propose a new trust region algorithm for solving the system of nonsmooth equations F(x) = 0 by using a smooth function satisfying the Jacobian consistency property to approximate the nonsmooth function F(x). Compared with existing trust region methods for systems of nonsmooth equations, the proposed algorithm possesses some nice convergence properties. Global convergence is established and, in particular, locally superlinear or quadratical convergence is obtained if F is semismooth or strongly semismooth at the solution.

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5

Izmailov, Alexey F., Alexey S. Kurennoy, and Mikhail V. Solodov. "The Josephy–Newton Method for Semismooth Generalized Equations and Semismooth SQP for Optimization." Set-Valued and Variational Analysis 21, no. 1 (July 18, 2012): 17–45. http://dx.doi.org/10.1007/s11228-012-0218-z.

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6

Zhou, Shui-sheng, Hong-wei Liu, Li-hua Zhou, and Feng Ye. "Semismooth Newton support vector machine." Pattern Recognition Letters 28, no. 15 (November 2007): 2054–62. http://dx.doi.org/10.1016/j.patrec.2007.06.010.

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7

Pickl, Stefan. "Solving the semismooth equivalence problem." European Journal of Operational Research 157, no. 1 (August 2004): 68–73. http://dx.doi.org/10.1016/j.ejor.2003.05.003.

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8

Potra, Florian A., Liqun Qi, and Defeng Sun. "Secant methods for semismooth equations." Numerische Mathematik 80, no. 2 (August 1, 1998): 305–24. http://dx.doi.org/10.1007/s002110050369.

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9

Bonettini, Silvia, and Federica Tinti. "A nonmonotone semismooth inexact Newton method." Optimization Methods and Software 22, no. 4 (August 2007): 637–57. http://dx.doi.org/10.1080/10556780601079258.

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10

Movahedian, Nooshin. "Nonsmooth Calculus of Semismooth Functions and Maps." Journal of Optimization Theory and Applications 160, no. 2 (September 5, 2013): 415–38. http://dx.doi.org/10.1007/s10957-013-0407-4.

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11

Tong, Xiaojiao, Dong-Hui Li, and Liqun Qi. "An iterative method for solving semismooth equations." Journal of Computational and Applied Mathematics 146, no. 1 (September 2002): 1–10. http://dx.doi.org/10.1016/s0377-0427(02)00413-2.

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12

Amstutz, Samuel. "A semismooth Newton method for topology optimization." Nonlinear Analysis: Theory, Methods & Applications 73, no. 6 (September 2010): 1585–95. http://dx.doi.org/10.1016/j.na.2010.04.065.

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13

Amat, S., and S. Busquier. "A modified secant method for semismooth equations." Applied Mathematics Letters 16, no. 6 (August 2003): 877–81. http://dx.doi.org/10.1016/s0893-9659(03)90011-5.

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14

Sun, Zhe, Jinping Zeng, and Hongru Xu. "Generalized Newton-iterative method for semismooth equations." Numerical Algorithms 58, no. 3 (March 26, 2011): 333–49. http://dx.doi.org/10.1007/s11075-011-9458-5.

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15

Chaney, Robin W. "Second-order necessary conditions in semismooth optimization." Mathematical Programming 40-40, no. 1-3 (January 1988): 95–109. http://dx.doi.org/10.1007/bf01580725.

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16

Ko, Chun-Hsu, and Jein-Shan Chen. "Optimal Grasping Manipulation for Multifingered Robots Using Semismooth Newton Method." Mathematical Problems in Engineering 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/681710.

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Multifingered robots play an important role in manipulation applications. They can grasp various shaped objects to perform point-to-point movement. It is important to plan the motion path of the object and appropriately control the grasping forces for multifingered robot manipulation. In this paper, we perform the optimal grasping control to find both optimal motion path of the object and minimum grasping forces in the manipulation. The rigid body dynamics of the object and the grasping forces subjected to the second-order cone (SOC) constraints are considered in optimal control problem. The minimum principle is applied to obtain the system equalities and the SOC complementarity problems. The SOC complementarity problems are further recast as the equations with the Fischer-Burmeister (FB) function. Since the FB function is semismooth, the semismooth Newton method with the generalized Jacobian of FB function is used to solve the nonlinear equations. The 2D and 3D simulations of grasping manipulation are performed to demonstrate the effectiveness of the proposed approach.

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17

Cao, Xi-Ren. "Semismooth Potentials of Stochastic Systems With Degenerate Diffusions." IEEE Transactions on Automatic Control 63, no. 10 (October 2018): 3566–72. http://dx.doi.org/10.1109/tac.2018.2800528.

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18

Munson, Todd S., Francisco Facchinei, Michael C. Ferris, Andreas Fischer, and Christian Kanzow. "The Semismooth Algorithm for Large Scale Complementarity Problems." INFORMS Journal on Computing 13, no. 4 (November 2001): 294–311. http://dx.doi.org/10.1287/ijoc.13.4.294.9734.

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19

Pang, J. S. "Frictional contact models with local compliance: semismooth formulation." ZAMM 88, no. 6 (June 5, 2008): 454–71. http://dx.doi.org/10.1002/zamm.200600039.

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20

Chaney, Robin W. "Second-Order Necessary Conditions in Constrained Semismooth Optimization." SIAM Journal on Control and Optimization 25, no. 4 (July 1987): 1072–81. http://dx.doi.org/10.1137/0325059.

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21

Münnich, Ralf T., Ekkehard W. Sachs, and Matthias Wagner. "Calibration of estimator-weights via semismooth Newton method." Journal of Global Optimization 52, no. 3 (August 4, 2011): 471–85. http://dx.doi.org/10.1007/s10898-011-9759-1.

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22

Lassonde, Marc. "Upper Semismooth Functions and the Subdifferential Determination Property." Set-Valued and Variational Analysis 26, no. 1 (January 3, 2018): 95–109. http://dx.doi.org/10.1007/s11228-017-0467-y.

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23

Ng, Michael K., Liqun Qi, Yu-fei Yang, and Yu-mei Huang. "On Semismooth Newton’s Methods for Total Variation Minimization." Journal of Mathematical Imaging and Vision 27, no. 3 (March 7, 2007): 265–76. http://dx.doi.org/10.1007/s10851-007-0650-0.

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24

Ulbrich, Michael. "A Multigrid Semismooth Newton Method for Semilinear Contact Problems." Journal of Computational Mathematics 35, no. 4 (June 2017): 486–528. http://dx.doi.org/10.4208/jcm.1702-m2016-0679.

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25

Ding, Liang, and Xueru Zhao. "Shearlet-Wavelet Regularized Semismooth Newton Iteration for Image Restoration." Mathematical Problems in Engineering 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/647254.

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Image normally has both dots-like and curve structures. But the traditional wavelet or multidirectional wave (ridgelet, contourlet, curvelet, etc.) could only restore one of these structures efficiently so that the restoration results for complex images are unsatisfactory. For the image restoration, this paper adopted a strategy of combined shearlet and wavelet frame and proposed a new restoration method. Theoretically, image sparse representation of dots-like and curve structures could be achieved by shearlet and wavelet, respectively. Under theL1regularization, the two frame-sparse structures could show their respective advantages and efficiently restore the two structures. In order to achieve superlinear convergence, this paper applied semismooth Newton method based on subgradient to solve objective functional without differentiability. Finally, through numerical results, the effectiveness of this strategy was validated, which presented outstanding advantages for any individual frame alone. Some detailed information that could not be restored in individual frame could be clearly demonstrated with this strategy.

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26

Pieraccini, S., M. G. Gasparo, and A. Pasquali. "Global Newton-type methods and semismooth reformulations for NCP." Applied Numerical Mathematics 44, no. 3 (February 2003): 367–84. http://dx.doi.org/10.1016/s0168-9274(02)00169-1.

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27

Daryina, A. N., and A. F. Izmailov. "Semismooth Newton method for quadratic programs with bound constraints." Computational Mathematics and Mathematical Physics 49, no. 10 (October 2009): 1706–16. http://dx.doi.org/10.1134/s0965542509100066.

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28

Pang, Zhi-Feng, and Yu-Fei Yang. "Semismooth Newton method for minimization of the LLT model." Inverse Problems & Imaging 3, no. 4 (2009): 677–91. http://dx.doi.org/10.3934/ipi.2009.3.677.

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29

Tong, Xiaojiao, Felix F. Wu, Yongping Zhang, Zheng Yan, and Yixin Ni. "A semismooth Newton method for solving optimal power flow." Journal of Industrial & Management Optimization 3, no. 3 (2007): 553–67. http://dx.doi.org/10.3934/jimo.2007.3.553.

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30

Hager, Corinna, and Barbara I. Wohlmuth. "Semismooth Newton methods for variational problems with inequality constraints." GAMM-Mitteilungen 33, no. 1 (April 2010): 8–24. http://dx.doi.org/10.1002/gamm.201010002.

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31

Wang, Changyu, Qian Liu, and Cheng Ma. "Smoothing SQP algorithm for semismooth equations with box constraints." Computational Optimization and Applications 55, no. 2 (December 20, 2012): 399–425. http://dx.doi.org/10.1007/s10589-012-9524-5.

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32

Chen, Xiaojun, Zuhair Nashed, and Liqun Qi. "Smoothing Methods and Semismooth Methods for Nondifferentiable Operator Equations." SIAM Journal on Numerical Analysis 38, no. 4 (January 2000): 1200–1216. http://dx.doi.org/10.1137/s0036142999356719.

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33

Chu, Dejun, Rui Lu, Jin Li, Xintong Yu, Changshui Zhang, and Qing Tao. "Optimizing Top- $k$ Multiclass SVM via Semismooth Newton Algorithm." IEEE Transactions on Neural Networks and Learning Systems 29, no. 12 (December 2018): 6264–75. http://dx.doi.org/10.1109/tnnls.2018.2826039.

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34

Chen, Zhongming, and Liqun Qi. "A semismooth Newton method for tensor eigenvalue complementarity problem." Computational Optimization and Applications 65, no. 1 (March 14, 2016): 109–26. http://dx.doi.org/10.1007/s10589-016-9838-9.

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35

Kanzow, Christian. "Inexact semismooth Newton methods for large-scale complementarity problems." Optimization Methods and Software 19, no. 3-4 (June 2004): 309–25. http://dx.doi.org/10.1080/10556780310001636369.

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36

Ulbrich, Michael. "Semismooth Newton Methods for Operator Equations in Function Spaces." SIAM Journal on Optimization 13, no. 3 (January 2002): 805–41. http://dx.doi.org/10.1137/s1052623400371569.

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37

Facchinei, Francisco, Andreas Fischer, and Christian Kanzow. "Regularity Properties of a Semismooth Reformulation of Variational Inequalities." SIAM Journal on Optimization 8, no. 3 (August 1998): 850–69. http://dx.doi.org/10.1137/s1052623496298194.

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38

Milzarek, Andre, Xiantao Xiao, Shicong Cen, Zaiwen Wen, and Michael Ulbrich. "A Stochastic Semismooth Newton Method for Nonsmooth Nonconvex Optimization." SIAM Journal on Optimization 29, no. 4 (January 2019): 2916–48. http://dx.doi.org/10.1137/18m1181249.

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39

Zhao, Hong-Jie, and Haijian Yang. "Semismooth Newton methods with domain decomposition for American options." Journal of Computational and Applied Mathematics 337 (August 2018): 37–50. http://dx.doi.org/10.1016/j.cam.2017.12.046.

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40

Studniarski, Marcin, and El Desouky Rahmo. "Approximating Clarke’s subgradients of semismooth functions by divided differences." Numerical Algorithms 43, no. 4 (February 20, 2007): 385–92. http://dx.doi.org/10.1007/s11075-007-9069-3.

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41

Zeng, Jinping, Zhe Sun, and Hongru Xu. "Semismooth Newton and Newton iterative methods for HJB equation." Journal of Computational and Applied Mathematics 235, no. 13 (May 2011): 3859–69. http://dx.doi.org/10.1016/j.cam.2011.01.032.

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42

Kong, Lingchen, and Qingmin Meng. "A semismooth Newton method for nonlinear symmetric cone programming." Mathematical Methods of Operations Research 76, no. 2 (May 16, 2012): 129–45. http://dx.doi.org/10.1007/s00186-012-0393-6.

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43

Gfrerer, Helmut, and Jiří V. Outrata. "On a Semismooth* Newton Method for Solving Generalized Equations." SIAM Journal on Optimization 31, no. 1 (January 2021): 489–517. http://dx.doi.org/10.1137/19m1257408.

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44

Wu, Jia, and Shougui Zhang. "Boundary Element and Augmented Lagrangian Methods for Contact Problem with Coulomb Friction." Mathematical Problems in Engineering 2020 (July 17, 2020): 1–10. http://dx.doi.org/10.1155/2020/7490736.

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In this paper, boundary element and augmented Lagrangian methods for Coulomb friction contact problems are presented. Based on the projection technique, both unilateral contact and Coulomb friction conditions are reformulated as fixed point problems. The original problem is deduced to a variational formulation with boundary integral operators. Then, we propose a new augmented Lagrangian method which can be dealt with the semismooth Newton method. Short theoretical results and the algorithm description are given. Numerical simulations show the performance of the method proposed.

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45

Pieraccini, S. "Hybrid Newton-Type Method for a Class of Semismooth Equations." Journal of Optimization Theory and Applications 112, no. 2 (February 2002): 381–402. http://dx.doi.org/10.1023/a:1013610108041.

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46

Stein, Oliver, and Aysun Tezel. "The Semismooth Approach for Semi-Infinite Programming without Strict Complementarity." SIAM Journal on Optimization 20, no. 2 (January 2009): 1052–72. http://dx.doi.org/10.1137/080719765.

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47

Schiela, Anton. "A Simplified Approach to Semismooth Newton Methods in Function Space." SIAM Journal on Optimization 19, no. 3 (January 2008): 1417–32. http://dx.doi.org/10.1137/060674375.

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48

Yin, Hongxia, Chen Ling, and Liqun Qi. "Smooth and Semismooth Newton Methods for Constrained Approximation and Estimation." Numerical Functional Analysis and Optimization 33, no. 5 (May 2012): 558–89. http://dx.doi.org/10.1080/01630563.2011.653071.

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49

Ito, Kazufumi, and Karl Kunisch. "Minimal Effort Problems and Their Treatment by Semismooth Newton Methods." SIAM Journal on Control and Optimization 49, no. 5 (January 2011): 2083–100. http://dx.doi.org/10.1137/100784667.

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50

Shi, Yueyong, Jian Huang, Yuling Jiao, and Qinglong Yang. "A Semismooth Newton Algorithm for High-Dimensional Nonconvex Sparse Learning." IEEE Transactions on Neural Networks and Learning Systems 31, no. 8 (August 2020): 2993–3006. http://dx.doi.org/10.1109/tnnls.2019.2935001.

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