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Globally Convergent Inexact Smoothing Newton Method for SOCCP

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Nonlinear Mathematics for Uncertainty and its Applications

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 100))

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Abstract

An inexact smoothing Newton method for solving second-order cone complementarity problems (SOCCP) is proposed. In each iteration the corresponding linear system is solved only approximately. Under mild assumptions, it is proved that the proposed method has global convergence and local superlinear convergence properties. Preliminary numerical results indicate that the method is effective for large-scale SOCCP.

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References

  1. Chen, J.S., Chen, X., Tseng, P.: Analysis of nonsmooth vector-valued functions associated with second-order cones. Mathematical Programming 101, 95–117 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  2. Facchinei, F., Kanzow, C.: A nonsmooth inexact Newton method for the solution of large-scale nonlinear complementarity problems. Mathematical Programming 76, 493–512 (1997)

    MathSciNet  MATH  Google Scholar 

  3. Fukushima, M., Luo, Z.Q., Tseng, P.: Smoothing functions for second-order-cone complementarity problems. SIAM Journal on Optimization 12, 436–460 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  4. Hayashi, S., Yamashita, N., Fukushima, M.: A combined smoothing and regularization method for monotone second-order cone complementarity problems. SIAM Journal on Optimization 15, 593–615 (2004)

    Article  MathSciNet  Google Scholar 

  5. Kanzow, C., Ferenczi, I., Fukushima, M.: On the local convergence of semismooth Newton methods for linear and nonlinear second-order cone programs without strict complementarity. SIAM Journal on Optimization 20, 297–320 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Lobo, M.S., Vandenberghe, L., Boyd, S., Lebret, H.: Applications of second-order cone programming. Linear Algebra and its Applications 284, 193–228 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  7. Rui, S.P., Xu, C.X.: Inexact non-interior continuation method for solving large-scale monotone SDCP. Applied Mathematics and Computation 215, 2521–2527 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Rui, S.P., Xu, C.X.: A smoothing inexact Newton method for nonlinear complementarity problems. Journal of Computational and Applied Mathematics 233, 2332–2338 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. Sun, D., Sun, J.: Strong semismoothness of the fischer-burmeister SDC and SOC complementarity functins. Mathematical Programming 103, 575-581 (2005)

    Google Scholar 

  10. Yoshise, A.: Interior point trajectories and a homogeneous model for nonliear complementarity problems over symmetric cones. SIAM Journal on Optimization 17, 1129–1153 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  11. Zhang, X.S., Liu, S.Y.: A smoothing method for second order cone complementarity problem. Journal of Computational and Applied Mathematics 228, 83–91 (2009)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Mathematical Science, Huaibei Normal University, Huaibei, 235000, People’s Republic of China

    Jie Zhang & Shao-Ping Rui

  2. Faculty of Science, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Shao-Ping Rui

Authors
  1. Jie Zhang
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  2. Shao-Ping Rui
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Editor information

Editors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, 100 Pingleyuan, 100124, Chaoyang District, Beijing, P.R. China

    Shoumei Li , Xia Wang  & Li Guan ,  & 

  2. Department of Systems Design and Informatics, Kyushu Institute of Technology, 680-4, Kawazu, 820-8502, lizuka, Japan

    Yoshiaki Okazaki

  3. Department of Mathematics, Shinshu University, 4-17-1 Wakasato, 380-8553, Nagano, Japan

    Jun Kawabe

  4. Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259-G3-47, Nagatsuta, Midori-ku, 226-8502, Yokohama, Japan

    Toshiaki Murofushi

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© 2011 Springer-Verlag Berlin Heidelberg

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Zhang, J., Rui, SP. (2011). Globally Convergent Inexact Smoothing Newton Method for SOCCP. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_52

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  • DOI: https://doi.org/10.1007/978-3-642-22833-9_52

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22832-2

  • Online ISBN: 978-3-642-22833-9

  • eBook Packages: EngineeringEngineering (R0)

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