ASQN beta 1.0

Structured quasi-Newton method for solving optimization with orthogonality constraint: [\min_X f(X); s.t. ; X^{\top}X = I_p, ] where X is a n-by-p matrix.

• The current version can be only used to solve problems from the electronic structure calculation and linear eigenvalue problem. However, it can be easily revised for other problems.

The electronic structure calculation

The code can cover the following two variants:

• Kohn-Sham total energy minimization
• Hartree-Fock total energy minimization

Running the codes requires a new version of the KSSOLV package [3]. Due to the copyright issues, KSSOLV is not provided.

Linear eigenvalue problems

The problem is: [\min \mathrm{Tr}(X^{\top}(A+B)[X]), s.t., X^{\top}X =I_p, ] where, $A$ and $B$ are two linear operators or matrices, the computatioal cost of $B[X]$ is much higher than that of $A[X]$.

• LOBPCG in [4] is used as a subroutine. Its specific license should be considered before modifying and/or redistributing them.

##References

1. Jiang Hu, Andre Milzarek, Zaiwen Wen, Yaxiang Yuan. Adaptive Quadratically Regularized Newton Method for Riemannian Optimization. SIAM Journal on Matrix Analysis and Applications
2. Jiang Hu, Bo Jiang, Lin Lin, Zaiwen Wen, Yaxiang Yuan. Structured Quasi-Newton Methods for Optimization with Orthogonality Constraints. arXiv preprint
3. Chao Yang, Juan C Meza, Byounghak Lee and Linwang, Wang. KSSOLV—a MATLAB toolbox for solving the Kohn-Sham equations. ACM Transactions on Mathematical Software
4. A. V. Knyazev. Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method, SIAM Journal on Scientific Computing 23 (2001), no. 2, pp. 517-541

The Authors

We hope that the method is useful for your application. If you have any bug reports or comments, please feel free to email one of the toolbox authors:

• Jiang Hu, jianghu at pku.edu.cn
• Zaiwen Wen, wenzw at pku.edu.cn

Copyright

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Copyright (C) 2018, Jiang Hu, Zaiwen Wen

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/