July  2015, 11(3): 733-746. doi: 10.3934/jimo.2015.11.733

An inexact semismooth Newton method for variational inequality with symmetric cone constraints

1. 

School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, Liaoning, China

2. 

Information and Engineering College, Dalian University, Dalian 116622, China

Received  September 2013 Revised  June 2014 Published  October 2014

In this paper, we consider using the inexact nonsmooth Newton method to efficiently solve the symmetric cone constrained variational inequality (VISCC) problem. It red provides a unified framework for dealing with the variational inequality with nonlinear constraints, variational inequality with the second-order cone constraints, and the variational inequality with semidefinite cone constraints. We get convergence of the above method and apply the results to three special types symmetric cones.
Citation: Shuang Chen, Li-Ping Pang, Dan Li. An inexact semismooth Newton method for variational inequality with symmetric cone constraints. Journal of Industrial & Management Optimization, 2015, 11 (3) : 733-746. doi: 10.3934/jimo.2015.11.733
References:
[1]

Optimization Letters, 6 (2012), 153-162. doi: 10.1007/s11590-010-0257-z.  Google Scholar

[2]

Mathematical and Computer Modelling, 55 (2012), 779-784. doi: 10.1016/j.mcm.2011.09.003.  Google Scholar

[3]

Computational Optimization and Applications, 25 (2003), 39-56. doi: 10.1023/A:1022996819381.  Google Scholar

[4]

Applied Mathematics and Optimization, 40 (1999), 19-37. doi: 10.1007/s002459900114.  Google Scholar

[5]

Vol. II. Springer Series in Operations Research. Springer-Verlag, New York, 2003.  Google Scholar

[6]

Oxford: Clarendon Press, New York, 1994.  Google Scholar

[7]

SIAM Journal on optimization, 12 (2002), 436-460. doi: 10.1137/S1052623400380365.  Google Scholar

[8]

Linear Algebra and Its Applications, 393 (2004), 203-232. doi: 10.1016/j.laa.2004.03.028.  Google Scholar

[9]

Acta Mathematica, 115 (1966), 271-310. doi: 10.1007/BF02392210.  Google Scholar

[10]

SIAM Journal on Optimization, 15 (2005), 593-615. doi: 10.1137/S1052623403421516.  Google Scholar

[11]

Mathematical Methods of Operations Research, 76 (2012), 129-145. doi: 10.1007/s00186-012-0393-6.  Google Scholar

[12]

SIAM Journal on Optimization, 19 (2008), 1028-1047. doi: 10.1137/060676775.  Google Scholar

[13]

Communications on Pure and Applied Mathematics, 20 (1967), 493-519. doi: 10.1002/cpa.3160200302.  Google Scholar

[14]

Applied Mathematics and Computation, 217 (2010), 2989-2999. doi: 10.1016/j.amc.2010.08.032.  Google Scholar

[15]

Journal of Optimization Theory and Applications, 9 (1972), 3-23. doi: 10.1007/BF00932801.  Google Scholar

[16]

Operations Research Letters, 38 (2010), 372-377. doi: 10.1016/j.orl.2010.07.011.  Google Scholar

[17]

Computational Optimization and Applications, 45 (2010), 59-88. doi: 10.1007/s10589-008-9166-9.  Google Scholar

[18]

Mathematics of operations research, 18 (1993), 227-244. doi: 10.1287/moor.18.1.227.  Google Scholar

[19]

Mathematical programming, 58 (1993), 353-367. doi: 10.1007/BF01581275.  Google Scholar

[20]

Mathematics of Operations Research, 33 (2008), 421-445. doi: 10.1287/moor.1070.0300.  Google Scholar

[21]

Computational Optimization and Applications, 51 (2012), 623-648. doi: 10.1007/s10589-010-9359-x.  Google Scholar

[22]

Optimization Methods and Software, 27 (2012), 445-459. doi: 10.1080/10556788.2010.534164.  Google Scholar

show all references

References:
[1]

Optimization Letters, 6 (2012), 153-162. doi: 10.1007/s11590-010-0257-z.  Google Scholar

[2]

Mathematical and Computer Modelling, 55 (2012), 779-784. doi: 10.1016/j.mcm.2011.09.003.  Google Scholar

[3]

Computational Optimization and Applications, 25 (2003), 39-56. doi: 10.1023/A:1022996819381.  Google Scholar

[4]

Applied Mathematics and Optimization, 40 (1999), 19-37. doi: 10.1007/s002459900114.  Google Scholar

[5]

Vol. II. Springer Series in Operations Research. Springer-Verlag, New York, 2003.  Google Scholar

[6]

Oxford: Clarendon Press, New York, 1994.  Google Scholar

[7]

SIAM Journal on optimization, 12 (2002), 436-460. doi: 10.1137/S1052623400380365.  Google Scholar

[8]

Linear Algebra and Its Applications, 393 (2004), 203-232. doi: 10.1016/j.laa.2004.03.028.  Google Scholar

[9]

Acta Mathematica, 115 (1966), 271-310. doi: 10.1007/BF02392210.  Google Scholar

[10]

SIAM Journal on Optimization, 15 (2005), 593-615. doi: 10.1137/S1052623403421516.  Google Scholar

[11]

Mathematical Methods of Operations Research, 76 (2012), 129-145. doi: 10.1007/s00186-012-0393-6.  Google Scholar

[12]

SIAM Journal on Optimization, 19 (2008), 1028-1047. doi: 10.1137/060676775.  Google Scholar

[13]

Communications on Pure and Applied Mathematics, 20 (1967), 493-519. doi: 10.1002/cpa.3160200302.  Google Scholar

[14]

Applied Mathematics and Computation, 217 (2010), 2989-2999. doi: 10.1016/j.amc.2010.08.032.  Google Scholar

[15]

Journal of Optimization Theory and Applications, 9 (1972), 3-23. doi: 10.1007/BF00932801.  Google Scholar

[16]

Operations Research Letters, 38 (2010), 372-377. doi: 10.1016/j.orl.2010.07.011.  Google Scholar

[17]

Computational Optimization and Applications, 45 (2010), 59-88. doi: 10.1007/s10589-008-9166-9.  Google Scholar

[18]

Mathematics of operations research, 18 (1993), 227-244. doi: 10.1287/moor.18.1.227.  Google Scholar

[19]

Mathematical programming, 58 (1993), 353-367. doi: 10.1007/BF01581275.  Google Scholar

[20]

Mathematics of Operations Research, 33 (2008), 421-445. doi: 10.1287/moor.1070.0300.  Google Scholar

[21]

Computational Optimization and Applications, 51 (2012), 623-648. doi: 10.1007/s10589-010-9359-x.  Google Scholar

[22]

Optimization Methods and Software, 27 (2012), 445-459. doi: 10.1080/10556788.2010.534164.  Google Scholar

[1]

Grace Nnennaya Ogwo, Chinedu Izuchukwu, Oluwatosin Temitope Mewomo. A modified extragradient algorithm for a certain class of split pseudo-monotone variational inequality problem. Numerical Algebra, Control & Optimization, 2021  doi: 10.3934/naco.2021011

[2]

Hong-Yi Miao, Li Wang. Preconditioned inexact Newton-like method for large nonsymmetric eigenvalue problems. Numerical Algebra, Control & Optimization, 2021  doi: 10.3934/naco.2021012

[3]

Li Chu, Bo Wang, Jie Zhang, Hong-Wei Zhang. Convergence analysis of a smoothing SAA method for a stochastic mathematical program with second-order cone complementarity constraints. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1863-1886. doi: 10.3934/jimo.2020050

[4]

Min Li. A three term Polak-Ribière-Polyak conjugate gradient method close to the memoryless BFGS quasi-Newton method. Journal of Industrial & Management Optimization, 2020, 16 (1) : 245-260. doi: 10.3934/jimo.2018149

[5]

Xiaoni Chi, Zhongping Wan, Zijun Hao. A full-modified-Newton step $ O(n) $ infeasible interior-point method for the special weighted linear complementarity problem. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021082

[6]

Fang Li, Jie Pan. On inner Poisson structures of a quantum cluster algebra without coefficients. Electronic Research Archive, , () : -. doi: 10.3934/era.2021021

[7]

Sergi Simon. Linearised higher variational equations. Discrete & Continuous Dynamical Systems, 2014, 34 (11) : 4827-4854. doi: 10.3934/dcds.2014.34.4827

[8]

Yuta Tanoue. Improved Hoeffding inequality for dependent bounded or sub-Gaussian random variables. Probability, Uncertainty and Quantitative Risk, 2021, 6 (1) : 53-60. doi: 10.3934/puqr.2021003

[9]

Krzysztof A. Krakowski, Luís Machado, Fátima Silva Leite. A unifying approach for rolling symmetric spaces. Journal of Geometric Mechanics, 2021, 13 (1) : 145-166. doi: 10.3934/jgm.2020016

[10]

Zhenbing Gong, Yanping Chen, Wenyu Tao. Jump and variational inequalities for averaging operators with variable kernels. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021045

[11]

Pablo D. Carrasco, Túlio Vales. A symmetric Random Walk defined by the time-one map of a geodesic flow. Discrete & Continuous Dynamical Systems, 2021, 41 (6) : 2891-2905. doi: 10.3934/dcds.2020390

[12]

Zehui Jia, Xue Gao, Xingju Cai, Deren Han. The convergence rate analysis of the symmetric ADMM for the nonconvex separable optimization problems. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1943-1971. doi: 10.3934/jimo.2020053

[13]

Reza Mazrooei-Sebdani, Zahra Yousefi. The coupled 1:2 resonance in a symmetric case and parametric amplification model. Discrete & Continuous Dynamical Systems - B, 2021, 26 (7) : 3737-3765. doi: 10.3934/dcdsb.2020255

[14]

Xue-Ping Luo, Yi-Bin Xiao, Wei Li. Strict feasibility of variational inclusion problems in reflexive Banach spaces. Journal of Industrial & Management Optimization, 2020, 16 (5) : 2495-2502. doi: 10.3934/jimo.2019065

[15]

Livia Betz, Irwin Yousept. Optimal control of elliptic variational inequalities with bounded and unbounded operators. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021009

[16]

Tomasz Kosmala, Markus Riedle. Variational solutions of stochastic partial differential equations with cylindrical Lévy noise. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 2879-2898. doi: 10.3934/dcdsb.2020209

[17]

Tao Wang. Variational relations for metric mean dimension and rate distortion dimension. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021050

[18]

Chiun-Chuan Chen, Hung-Yu Chien, Chih-Chiang Huang. A variational approach to three-phase traveling waves for a gradient system. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021055

[19]

Jianxun Liu, Shengjie Li, Yingrang Xu. Quantitative stability of the ERM formulation for a class of stochastic linear variational inequalities. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021083

[20]

Mao Okada. Local rigidity of certain actions of solvable groups on the boundaries of rank-one symmetric spaces. Journal of Modern Dynamics, 2021, 17: 111-143. doi: 10.3934/jmd.2021004

2019 Impact Factor: 1.366

Metrics

  • PDF downloads (83)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]