[1]
|
P. A. Absil, R. Mahony and R. Sepulchre, Optimization Algorithms on Matrix Manifolds, Princeton University Press, Princeton, 2008.
doi: 10.1515/9781400830244.
|
[2]
|
T. Abrudan, J. Eriksson and V. Koivunen, Steepest descent algorithms for optimization under unitary matrix constraint, IEEE Transactions on Signal Processing, 56 (2008), 1134-1147.
doi: 10.1109/TSP.2007.908999.
|
[3]
|
J. Barzilai and J. M. Borwein, Two-point step size gradient methods, IMA Journal of Numerical Analysis, 8 (1988), 141-148.
doi: 10.1093/imanum/8.1.141.
|
[4]
|
A. D'Aspremont, L. E. Ghaoui and J. G. R. G. Lanckriet, A direct formulation for sparse PCA using semidefinite programming, SIAM Review, 49 (2007), 434-448.
doi: 10.1137/050645506.
|
[5]
|
Y. Dai and R. Fletcher, Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming, Numerische Mathematik, 100 (2005), 21-47.
doi: 10.1007/s00211-004-0569-y.
|
[6]
|
L. Eldén and H. Park, A procrustes problem on the Stiefel manifold, Numerische Mathematik, 82 (1999), 599-619.
doi: 10.1007/s002110050432.
|
[7]
|
A. Edelman, T. A. Arias and S. T. Smith, The geometry of algorithms with orthogonality constraints, SIAM Journal on Matrix Analysis and Applications, 20 (1998), 303-353.
doi: 10.1137/S0895479895290954.
|
[8]
|
B. Gao, X. Liu, X. Chen and Y. Yuan, A new first-order algorithmic framework for optimization problems with orthogonality constraints, SIAM Journal on Optimization, 28 (2018), 302-332.
doi: 10.1137/16M1098759.
|
[9]
|
J. Hu, B. Jiang and X. Liu et al, A note on semidefinite programming relaxations for polynomial optimization over a single sphere, Science China Mathematics, 59 (2016), 1543-1560.
doi: 10.1007/s11425-016-0301-5.
|
[10]
|
B. Jiang and Y. Dai, A framework of constraint preserving update schemes for optimization on Stiefel manifold, Mathematical Programming, 153 (2015), 535-575.
doi: 10.1007/s10107-014-0816-7.
|
[11]
|
X. Liu, C. Hao and M. Cheng, A sequential subspace projection method for linear symmetric eigenvalue problem, Asia-Pacific Journal of Operational Research, 30 (2013), 1340003.1-1340003.17.
doi: 10.1142/S0217595913400034.
|
[12]
|
X. Liu, X. Wang and Z. Wen et al, On the convergence of the self-consistent field iteration in Kohn-Sham density functional theory, SIAM Journal on Matrix Analysis and Applications, 35 (2014), 546-558.
doi: 10.1137/130911032.
|
[13]
|
Y. Nishimori and S. Akaho, Learning algorithms utilizing quasi-geodesic flows on the Stiefel manifold, Neurocomputing, 67 (2005), 106-135.
|
[14]
|
A. Sameh and Z. Tong, The trace minimization method for the symmetric generalized eigenvalue problem, Journal of Computational and Applied Mathematics, 123 (2000), 155-175.
doi: 10.1016/S0377-0427(00)00391-5.
|
[15]
|
M. Ulbrich, Z. Wen and C. Yang et al, A proximal gradient method for ensemble density functional theory, SIAM Journal on Scientific Computing, 37 (2015), A1975–A2002.
doi: 10.1137/14098973X.
|
[16]
|
Z. Wen and W. Yin, A feasible method for optimization with orthogonality constraints, Mathematical Programming, 142 (2013), 397-434.
doi: 10.1007/s10107-012-0584-1.
|
[17]
|
C. Yang, J. C. Meza and L. Wang, A constrained optimization algorithm for total energy minimization in electronic structure calculations, Journal of Computational Physics, 217 (2006), 709-721.
doi: 10.1016/j.jcp.2006.01.030.
|
[18]
|
C. Yang, J. C. Meza and B. Lee et al, KSSOLV-a MATLAB toolbox for solving the Kohn-Sham equations, ACM Transactions on Mathematical Software, 36 (2009), 1-35.
doi: 10.1145/1499096.1499099.
|
[19]
|
H. Zhang and W. W. Hager, A nonmonotone line search technique and its application to unconstrained optimization, SIAM Journal on Optimization, 14 (2004), 1043-1056.
doi: 10.1137/S1052623403428208.
|
[20]
|
H. Zou, T. Hastie and R. Tibshirani, Sparse principal component analysis, Journal of Computational and Graphical Statistics, 15 (2006), 265-286.
doi: 10.1198/106186006X113430.
|
[21]
|
X. Zhang, J. Zhu and Z. Wen, Gradient type optimization methods for electronic structure calculations, SIAM Journal on Scientific Computing, 36 (2014), A265–A289.
doi: 10.1137/130932934.
|