|
|
|
Convergence of an augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints |
Jin GUO, Suxiang HE( ) |
| School of Science, Wuhan University of Technology, Wuhan 430070, China |
|
|
|
|
Abstract An augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints is proposed based on a Löwner operator associated with a potential function for the optimization problems with inequality constraints. The favorable properties of both the Löwner operator and the corresponding augmented Lagrangian are discussed. And under some mild assumptions, the rate of convergence of the augmented Lagrange algorithm is studied in detail.
|
| Keywords
Potential function
Löwner operator
augmented Lagrange algorithm
nonlinear second-order cone optimizations
|
|
Corresponding Author(s):
Suxiang HE
|
|
Issue Date: 19 May 2022
|
|
| 1 |
F Alizadeh , D Goldfarb . Second-order cone programming. Mathematical Programming, 2003, 95 (1): 3- 51
https://doi.org/10.1007/s10107-002-0339-5
|
| 2 |
J F Bonnans , C H Ramírez . Perturbation analysis of second-order cone programming problems. Mathematical Programming, 2005, 104 (2): 205- 227
|
| 3 |
J F Bonnans , A Shapiro . Perturbation Analysis of Optimization Problems. New York: Springer-Verlag, 2000
|
| 4 |
G Debreu . Definite and semidefinite quadratic forms. Econometrica, 1952, 20: 295- 300
https://doi.org/10.2307/1907852
|
| 5 |
J Faraut , A Korányi . Analysis on Symmetric Cones. Oxford: Clarendon Press, 1994
|
| 6 |
J Gu , L W Zhang , X T Xiao . Log-Sigmoid nonlinear Lagrange method for nonlinear optimization problems over second-order cones. Journal of Computational and Applied Mathematics, 2009, 229 (1): 129- 144
https://doi.org/10.1016/j.cam.2008.10.016
|
| 7 |
S X He , L W Zhang , X S Li . A Potential Function for Solving Inequality Constrained Optimiztion Problems. Advances in Mathematics (China), 2004, 33 (3): 343- 351
|
| 8 |
M R Hestenes . Multiplier and gradient methods. Journal of Optimization Theory and Applications, 1969, 4 (5): 303- 320
https://doi.org/10.1007/BF00927673
|
| 9 |
Y J Liu , L W Zhang . Convergence of the Augmented Lagrangian Method for Nonlinear Optimization Problems over Second-Order Cones. Journal of Optimization Theory and Applications, 2008, 139 (3): 557- 575
https://doi.org/10.1007/s10957-008-9390-6
|
| 10 |
M S Lobo , L Vandenberghe , S Boyd , H Lebret . Applications of second-order cone programming. Linear Algebra and its Applications, 1998, 284 (1): 193- 228
|
| 11 |
J M Lou , Q B Zhong . Cooperative motion control method for humanoid robot. Journal of Beijing University of Posts and Telecommunications, 2017, 40 (3): 123- 126 (in Chinese)
|
| 12 |
R A Polyak . Log-Sigmoid multipliers method in constrained optimization. Annals of Operations Research, 2001, 101 (1): 427- 460
|
| 13 |
M J D Powell . A Method for Nonlinear Constraints in Minimization Problems. Optimization, 1969: 283- 298
|
| 14 |
R T Rockafellar . A dual approach to solving nonlinear programming problems by unconstrained optimization. Mathematical Programming, 1973, 5 (1): 354- 373
https://doi.org/10.1007/BF01580138
|
| 15 |
R T Rockafellar . Augmented Lagrange Multiplier Functions and Duality in Nonconvex Programming. SIAM Journal on Control, 1974, 12 (2): 268- 285
https://doi.org/10.1137/0312021
|
| 16 |
L W Zhang , J Gu , X T Xiao . A class of nonlinear Lagrangians for nonconvex second order cone programming. Computational Optimization and Applications, 2011, 49 (1): 61- 99
https://doi.org/10.1007/s10589-009-9279-9
|
| 17 |
L W Zhang , Y H Ren , Y Wu , X T Xiao . A class of nonlinear Lagrangians: theory and algorithm. Asia-Pacific Journal of Operational Research, 2008, 25 (3): 327- 371
https://doi.org/10.1142/S021759590800178X
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
| |
Shared |
|
|
|
|
| |
Discussed |
|
|
|
|
