Paper Info
Title
A SemiSmooth Newton Method for Semidefinite Programs and its Applications in Electronic Structure Calculations.
Abstract
The well-known interior point method for semidefinite progams can only be used to tackle problems of relatively small scales. First-order methods such as the the alternating direction method of multipliers (ADMM) have much lower computational cost per iteration. However, their convergence can be slow, especially for obtaining highly accurate approximations. In this paper, we present a practical and efficient second-order semismooth Newton type method based on solving a fixed-point mapping derived from an equivalent form of the ADMM. We discuss a number of techniques that can be used to improve the computational efficiency of the method and achieve global convergence. Then we further consider the application in electronic structure calculations. The ground state energy of a many-electron system can be approximated by an variational approach in which the total energy of the system is minimized with respect to one- and two-body reduced density matrices instead of many-electron wavefunctions. This problem can be formulated as a semidefinite programming problem. Extensive numerical experiments show that our approach is competitive to the state-of-the-art methods in terms of both accuracy and speed.
Year
DOI
Venue
2018
10.1137/18M1188069
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Keywords
Field
DocType
semidefinite programming,ADMM,semismooth Newton method,electronic structure calculation,two-body reduced density matrix
Applied mathematics,Mathematical optimization,Electronic structure,Interior point method,Semidefinite programming,Mathematics,Newton's method
Journal
Volume
Issue
ISSN
40
6
1064-8275
Citations 
PageRank 
References 
1
0.37
0
Authors
4
Name
Order
Citations
PageRank
Yongfeng Li110.37
Zaiwen Wen293440.20
Chao Yang3141.35
Y. Yuan4982146.16