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Title: Jacobian consistency of a one-parametric class of smoothing Fischer–Burmeister functions for SOCCP

Abstract

The Jacobian consistency of smoothing functions plays an important role for achieving the rapid convergence of Newton methods or Newton-like methods with an appropriate parameter control. In this paper, we study the properties, derive the computable formula for the Jacobian matrix and prove the Jacobian consistency of a one-parametric class of smoothing Fischer–Burmeister functions for second-order cone complementarity problems proposed by Tang et al. (Comput Appl Math 33:655–669, 2014). Then we apply its Jacobian consistency to a smoothing Newton method with the appropriate parameter control presented by Chen et al. (Math Comput 67:519–540, 1998), and show the global convergence and local quadratic convergence of the algorithm for solving the SOCCP under rather weak assumptions.

Authors:
 [1];  [2];  [3];  [4]
  1. Guilin University of Electronic Technology, School of Mathematics and Computing Science, Guangxi Key Laboratory of Automatic Detecting Technology and Instruments (China)
  2. Guilin University of Electronic Technology, School of Mathematics and Computing Science, Guangxi Key Laboratory of Cryptography and Information Security (China)
  3. Guilin University of Electronic Technology, School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation (China)
  4. Wuhan University, School of Mathematics and Statistics (China)
Publication Date:
OSTI Identifier:
22769379
Resource Type:
Journal Article
Journal Name:
Computational and Applied Mathematics
Additional Journal Information:
Journal Volume: 37; Journal Issue: 1; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; CONVERGENCE; FUNCTIONS; MATRICES; NEWTON METHOD

Citation Formats

Chi, Xiaoni, Wang, Yang, Zhu, Zhibin, and Wan, Zhongping. Jacobian consistency of a one-parametric class of smoothing Fischer–Burmeister functions for SOCCP. United States: N. p., 2018. Web. doi:10.1007/S40314-016-0352-6.
Chi, Xiaoni, Wang, Yang, Zhu, Zhibin, & Wan, Zhongping. Jacobian consistency of a one-parametric class of smoothing Fischer–Burmeister functions for SOCCP. United States. doi:10.1007/S40314-016-0352-6.
Chi, Xiaoni, Wang, Yang, Zhu, Zhibin, and Wan, Zhongping. Thu . "Jacobian consistency of a one-parametric class of smoothing Fischer–Burmeister functions for SOCCP". United States. doi:10.1007/S40314-016-0352-6.
@article{osti_22769379,
title = {Jacobian consistency of a one-parametric class of smoothing Fischer–Burmeister functions for SOCCP},
author = {Chi, Xiaoni and Wang, Yang and Zhu, Zhibin and Wan, Zhongping},
abstractNote = {The Jacobian consistency of smoothing functions plays an important role for achieving the rapid convergence of Newton methods or Newton-like methods with an appropriate parameter control. In this paper, we study the properties, derive the computable formula for the Jacobian matrix and prove the Jacobian consistency of a one-parametric class of smoothing Fischer–Burmeister functions for second-order cone complementarity problems proposed by Tang et al. (Comput Appl Math 33:655–669, 2014). Then we apply its Jacobian consistency to a smoothing Newton method with the appropriate parameter control presented by Chen et al. (Math Comput 67:519–540, 1998), and show the global convergence and local quadratic convergence of the algorithm for solving the SOCCP under rather weak assumptions.},
doi = {10.1007/S40314-016-0352-6},
journal = {Computational and Applied Mathematics},
issn = {0101-8205},
number = 1,
volume = 37,
place = {United States},
year = {2018},
month = {3}
}