-
Previous Article
Optimal capacity reservation policy on innovative product
- JIMO Home
- This Issue
-
Next Article
Pricing and replenishment strategy for a multi-market deteriorating product with time-varying and price-sensitive demand
A smoothing-type algorithm for absolute value equations
1. | Department of Public Basic, Wuhan Yangtze Business University, Wuhan 430065, China |
2. | Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, China |
References:
[1] |
L. Caccetta, B. Qu and G. L. Zhou, A globally and quadratically convergent method for absolute value equations,, Computational Optimization and Applications, 48 (2011), 45.
doi: 10.1007/s10589-009-9242-9. |
[2] |
R. W. Cottle, J. S. Pang and R. E. Stone, "The Linear Complementarity Problem,", Academic Press, (1992).
|
[3] |
N. J. Higham, Estimating the matrix $p$-norm,, Numerische Mathematik, 62 (1992), 539.
doi: 10.1007/BF01396242. |
[4] |
R. A. Horn and C. R. Johnson, "Matrix Analysis,", Cambridge University Press, (1985).
|
[5] |
S. L. Hu and Z. H. Huang, A note on absolute value equations,, Optimization Letters, 4 (2010), 417.
doi: 10.1007/s11590-009-0169-y. |
[6] |
S. L. Hu, Z. H. Huang and J. S. Chen, Properties of a family of generalized NCP-functions and a derivative free algorithm for complementarity problems,, Journal of Computational and Applied Mathematics, 230 (2009), 69.
doi: 10.1016/j.cam.2008.10.056. |
[7] |
S. L. Hu, Z. H. Huang and Q. Zhang, A generalized Newton method for absolute value equations associated with second order cones,, Journal of Computational and Applied Mathematics, 235 (2011), 1490.
doi: 10.1016/j.cam.2010.08.036. |
[8] |
Z. H. Huang, Locating a maximally complementary solution of the monotone NCP by using non-interior-point smoothing algorithms,, Mathematical Methods of Operations Research, 61 (2005), 41.
doi: 10.1007/s001860400384. |
[9] |
Z. H. Huang, Y. Zhang and W. Wu, A smoothing-type algorithm for solving system of inequalities,, Journal of Computational and Applied Mathematics, 220 (2008), 355.
doi: 10.1016/j.cam.2007.08.024. |
[10] |
O. L. Mangasarian, Absolute value programming,, Computational Optimization and Applications, 36 (2007), 43. Google Scholar |
[11] |
O. L. Mangasarian, Absolute value equation solution via concave minmization,, Optimization Letters, 1 (2007), 3.
doi: 10.1007/s11590-006-0005-6. |
[12] |
O. L. Mangasarian, A generalized Newton method for absolute value equations,, Optimization Letters, 3 (2009), 101.
doi: 10.1007/s11590-008-0094-5. |
[13] |
O. L. Mangasarian and R. R. Meyer, Absolute value equations,, Linear Algebra and Its Applications, 419 (2006), 359.
doi: 10.1016/j.laa.2006.05.004. |
[14] |
O. A. Prokopyev, On equivalent reformulations for absolute value equations,, Computational Optimization and Applications, 44 (2009), 363.
doi: 10.1007/s10589-007-9158-1. |
[15] |
O. A. Prokopyev, S. Butenko and A. Trapp, Checking solvability of systems of interval linear equations and inequalities via mixed integer programming,, European Journal of Operational Research, 199 (2009), 117.
doi: 10.1016/j.ejor.2008.11.008. |
[16] |
L. Qi, Convergence analysis of some algorithms for solving nonsmooth equations,, Mathematics of Operations Research, 18 (1993), 227.
doi: 10.1287/moor.18.1.227. |
[17] |
L. Qi, D. Sun and G. L. Zhou, A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequality problems,, Mathematical Programming, 87 (2000), 1.
|
[18] |
J. Rohn, A theorem of the alternatives for the equation $Ax+B|x|=b$,, Linear and Multilinear Algebra, 52 (2004), 421.
doi: 10.1080/0308108042000220686. |
[19] |
J. Rohn, Solvability of systems of interval linear equations and inequalities,, in, (2006), 35.
doi: 10.1007/0-387-32698-7_2. |
[20] |
J. Rohn, An algorithm for solving the absolute value equation,, Eletronic Journal of Linear Algebra, 18 (2009), 589.
|
[21] |
C. Zhang and Q. J. Wei, Global and finite convergence of a generalized Newton method for absolute value equations,, Journal of Optimization Theory and Applications, 143 (2009), 391.
doi: 10.1007/s10957-009-9557-9. |
show all references
References:
[1] |
L. Caccetta, B. Qu and G. L. Zhou, A globally and quadratically convergent method for absolute value equations,, Computational Optimization and Applications, 48 (2011), 45.
doi: 10.1007/s10589-009-9242-9. |
[2] |
R. W. Cottle, J. S. Pang and R. E. Stone, "The Linear Complementarity Problem,", Academic Press, (1992).
|
[3] |
N. J. Higham, Estimating the matrix $p$-norm,, Numerische Mathematik, 62 (1992), 539.
doi: 10.1007/BF01396242. |
[4] |
R. A. Horn and C. R. Johnson, "Matrix Analysis,", Cambridge University Press, (1985).
|
[5] |
S. L. Hu and Z. H. Huang, A note on absolute value equations,, Optimization Letters, 4 (2010), 417.
doi: 10.1007/s11590-009-0169-y. |
[6] |
S. L. Hu, Z. H. Huang and J. S. Chen, Properties of a family of generalized NCP-functions and a derivative free algorithm for complementarity problems,, Journal of Computational and Applied Mathematics, 230 (2009), 69.
doi: 10.1016/j.cam.2008.10.056. |
[7] |
S. L. Hu, Z. H. Huang and Q. Zhang, A generalized Newton method for absolute value equations associated with second order cones,, Journal of Computational and Applied Mathematics, 235 (2011), 1490.
doi: 10.1016/j.cam.2010.08.036. |
[8] |
Z. H. Huang, Locating a maximally complementary solution of the monotone NCP by using non-interior-point smoothing algorithms,, Mathematical Methods of Operations Research, 61 (2005), 41.
doi: 10.1007/s001860400384. |
[9] |
Z. H. Huang, Y. Zhang and W. Wu, A smoothing-type algorithm for solving system of inequalities,, Journal of Computational and Applied Mathematics, 220 (2008), 355.
doi: 10.1016/j.cam.2007.08.024. |
[10] |
O. L. Mangasarian, Absolute value programming,, Computational Optimization and Applications, 36 (2007), 43. Google Scholar |
[11] |
O. L. Mangasarian, Absolute value equation solution via concave minmization,, Optimization Letters, 1 (2007), 3.
doi: 10.1007/s11590-006-0005-6. |
[12] |
O. L. Mangasarian, A generalized Newton method for absolute value equations,, Optimization Letters, 3 (2009), 101.
doi: 10.1007/s11590-008-0094-5. |
[13] |
O. L. Mangasarian and R. R. Meyer, Absolute value equations,, Linear Algebra and Its Applications, 419 (2006), 359.
doi: 10.1016/j.laa.2006.05.004. |
[14] |
O. A. Prokopyev, On equivalent reformulations for absolute value equations,, Computational Optimization and Applications, 44 (2009), 363.
doi: 10.1007/s10589-007-9158-1. |
[15] |
O. A. Prokopyev, S. Butenko and A. Trapp, Checking solvability of systems of interval linear equations and inequalities via mixed integer programming,, European Journal of Operational Research, 199 (2009), 117.
doi: 10.1016/j.ejor.2008.11.008. |
[16] |
L. Qi, Convergence analysis of some algorithms for solving nonsmooth equations,, Mathematics of Operations Research, 18 (1993), 227.
doi: 10.1287/moor.18.1.227. |
[17] |
L. Qi, D. Sun and G. L. Zhou, A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequality problems,, Mathematical Programming, 87 (2000), 1.
|
[18] |
J. Rohn, A theorem of the alternatives for the equation $Ax+B|x|=b$,, Linear and Multilinear Algebra, 52 (2004), 421.
doi: 10.1080/0308108042000220686. |
[19] |
J. Rohn, Solvability of systems of interval linear equations and inequalities,, in, (2006), 35.
doi: 10.1007/0-387-32698-7_2. |
[20] |
J. Rohn, An algorithm for solving the absolute value equation,, Eletronic Journal of Linear Algebra, 18 (2009), 589.
|
[21] |
C. Zhang and Q. J. Wei, Global and finite convergence of a generalized Newton method for absolute value equations,, Journal of Optimization Theory and Applications, 143 (2009), 391.
doi: 10.1007/s10957-009-9557-9. |
[1] |
Zheng-Hai Huang, Nan Lu. Global and global linear convergence of smoothing algorithm for the Cartesian $P_*(\kappa)$-SCLCP. Journal of Industrial & Management Optimization, 2012, 8 (1) : 67-86. doi: 10.3934/jimo.2012.8.67 |
[2] |
Zheng-Hai Huang, Shang-Wen Xu. Convergence properties of a non-interior-point smoothing algorithm for the P*NCP. Journal of Industrial & Management Optimization, 2007, 3 (3) : 569-584. doi: 10.3934/jimo.2007.3.569 |
[3] |
Fakhrodin Hashemi, Saeed Ketabchi. Numerical comparisons of smoothing functions for optimal correction of an infeasible system of absolute value equations. Numerical Algebra, Control & Optimization, 2020, 10 (1) : 13-21. doi: 10.3934/naco.2019029 |
[4] |
Chunlin Hao, Xinwei Liu. Global convergence of an SQP algorithm for nonlinear optimization with overdetermined constraints. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 19-29. doi: 10.3934/naco.2012.2.19 |
[5] |
Liping Zhang, Soon-Yi Wu, Shu-Cherng Fang. Convergence and error bound of a D-gap function based Newton-type algorithm for equilibrium problems. Journal of Industrial & Management Optimization, 2010, 6 (2) : 333-346. doi: 10.3934/jimo.2010.6.333 |
[6] |
Zhong Tan, Qiuju Xu, Huaqiao Wang. Global existence and convergence rates for the compressible magnetohydrodynamic equations without heat conductivity. Discrete & Continuous Dynamical Systems - A, 2015, 35 (10) : 5083-5105. doi: 10.3934/dcds.2015.35.5083 |
[7] |
Ruiying Wei, Yin Li, Zheng-an Yao. Global existence and convergence rates of solutions for the compressible Euler equations with damping. Discrete & Continuous Dynamical Systems - B, 2020, 25 (8) : 2949-2967. doi: 10.3934/dcdsb.2020047 |
[8] |
Shuhua Wang, Zhenlong Chen, Baohuai Sheng. Convergence of online pairwise regression learning with quadratic loss. Communications on Pure & Applied Analysis, 2020, 19 (8) : 4023-4054. doi: 10.3934/cpaa.2020178 |
[9] |
Yi Zhang, Liwei Zhang, Jia Wu. On the convergence properties of a smoothing approach for mathematical programs with symmetric cone complementarity constraints. Journal of Industrial & Management Optimization, 2018, 14 (3) : 981-1005. doi: 10.3934/jimo.2017086 |
[10] |
J. Frédéric Bonnans, Justina Gianatti, Francisco J. Silva. On the convergence of the Sakawa-Shindo algorithm in stochastic control. Mathematical Control & Related Fields, 2016, 6 (3) : 391-406. doi: 10.3934/mcrf.2016008 |
[11] |
Olivier Bokanowski, Maurizio Falcone, Roberto Ferretti, Lars Grüne, Dante Kalise, Hasnaa Zidani. Value iteration convergence of $\epsilon$-monotone schemes for stationary Hamilton-Jacobi equations. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9) : 4041-4070. doi: 10.3934/dcds.2015.35.4041 |
[12] |
Qiyu Jin, Ion Grama, Quansheng Liu. Convergence theorems for the Non-Local Means filter. Inverse Problems & Imaging, 2018, 12 (4) : 853-881. doi: 10.3934/ipi.2018036 |
[13] |
Aibin Zang. Kato's type theorems for the convergence of Euler-Voigt equations to Euler equations with Drichlet boundary conditions. Discrete & Continuous Dynamical Systems - A, 2019, 39 (9) : 4945-4953. doi: 10.3934/dcds.2019202 |
[14] |
Stefan Kindermann, Antonio Leitão. Convergence rates for Kaczmarz-type regularization methods. Inverse Problems & Imaging, 2014, 8 (1) : 149-172. doi: 10.3934/ipi.2014.8.149 |
[15] |
Qiao Liu. Local rigidity of certain solvable group actions on tori. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 553-567. doi: 10.3934/dcds.2020269 |
[16] |
Stefano Scrobogna. Global existence and convergence of nondimensionalized incompressible Navier-Stokes equations in low Froude number regime. Discrete & Continuous Dynamical Systems - A, 2020, 40 (9) : 5471-5511. doi: 10.3934/dcds.2020235 |
[17] |
Chun-Hsiung Hsia, Chang-Yeol Jung, Bongsuk Kwon. On the global convergence of frequency synchronization for Kuramoto and Winfree oscillators. Discrete & Continuous Dynamical Systems - B, 2019, 24 (7) : 3319-3334. doi: 10.3934/dcdsb.2018322 |
[18] |
Ye Tian, Cheng Lu. Nonconvex quadratic reformulations and solvable conditions for mixed integer quadratic programming problems. Journal of Industrial & Management Optimization, 2011, 7 (4) : 1027-1039. doi: 10.3934/jimo.2011.7.1027 |
[19] |
X. X. Huang, D. Li, Xiaoqi Yang. Convergence of optimal values of quadratic penalty problems for mathematical programs with complementarity constraints. Journal of Industrial & Management Optimization, 2006, 2 (3) : 287-296. doi: 10.3934/jimo.2006.2.287 |
[20] |
Kien Ming Ng, Trung Hieu Tran. A parallel water flow algorithm with local search for solving the quadratic assignment problem. Journal of Industrial & Management Optimization, 2019, 15 (1) : 235-259. doi: 10.3934/jimo.2018041 |
2019 Impact Factor: 1.366
Tools
Metrics
Other articles
by authors
[Back to Top]