TY - JOUR
T1 - Nonconvex and Nonsmooth Optimization with Generalized Orthogonality Constraints
T2 - An Approximate Augmented Lagrangian Method
AU - Zhu, Hong
AU - Zhang, Xiaowei
AU - Chu, Delin
AU - Liao, Lizhi
N1 - Publisher Copyright:
© 2017, Springer Science+Business Media New York.
PY - 2017/7
Y1 - 2017/7
N2 - Nonconvex and nonsmooth optimization problems with linear equation and generalized orthogonality constraints have wide applications. These problems are difficult to solve due to nonsmooth objective function and nonconvex constraints. In this paper, by introducing an extended proximal alternating linearized minimization (EPALM) method, we propose a framework based on the augmented Lagrangian scheme (EPALMAL). We also show that the EPALMAL method has global convergence in the sense that every bounded sequence generated by the EPALMAL method has at least one convergent subsequence that converges to the Karush–Kuhn–Tucker point of the original problem. Experiments on a variety of applications, including compressed modes and multivariate data analysis, have demonstrated that the proposed method is noticeably efficient and achieves comparable performance with existing methods.
AB - Nonconvex and nonsmooth optimization problems with linear equation and generalized orthogonality constraints have wide applications. These problems are difficult to solve due to nonsmooth objective function and nonconvex constraints. In this paper, by introducing an extended proximal alternating linearized minimization (EPALM) method, we propose a framework based on the augmented Lagrangian scheme (EPALMAL). We also show that the EPALMAL method has global convergence in the sense that every bounded sequence generated by the EPALMAL method has at least one convergent subsequence that converges to the Karush–Kuhn–Tucker point of the original problem. Experiments on a variety of applications, including compressed modes and multivariate data analysis, have demonstrated that the proposed method is noticeably efficient and achieves comparable performance with existing methods.
KW - Augmented Lagrangian scheme
KW - Generalized orthogonality constraints
KW - Linearization
KW - Proximal alternating minimization method
UR - http://www.scopus.com/inward/record.url?scp=85009887601&partnerID=8YFLogxK
U2 - 10.1007/s10915-017-0359-1
DO - 10.1007/s10915-017-0359-1
M3 - Journal article
AN - SCOPUS:85009887601
SN - 0885-7474
VL - 72
SP - 331
EP - 372
JO - Journal of Scientific Computing
JF - Journal of Scientific Computing
IS - 1
ER -