research-article

A SemiSmooth Newton Method for Semidefinite Programs and its Applications in Electronic Structure Calculations

Authors: Yongfeng Li, Zaiwen Wen, Chao Yang, Ya-xiang YuanAuthors Info & Claims

SIAM Journal on Scientific Computing, Volume 40, Issue 6

Pages A4131 - A4157

https://doi.org/10.1137/18M1188069

Published: 01 January 2018 Publication History

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.

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Cited By

Deng ZDeng KHu JWen Z(2025)An Augmented Lagrangian Primal-Dual Semismooth Newton Method for Multi-Block Composite OptimizationJournal of Scientific Computing10.1007/s10915-025-02794-4102:3Online publication date: 1-Mar-2025
https://dl.acm.org/doi/10.1007/s10915-025-02794-4
Zhang RLiu XDai Y(2024)IPRSDP: a primal-dual interior-point relaxation algorithm for semidefinite programmingComputational Optimization and Applications10.1007/s10589-024-00558-888:1(1-36)Online publication date: 1-May-2024
https://dl.acm.org/doi/10.1007/s10589-024-00558-8

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cover image SIAM Journal on Scientific Computing

SIAM Journal on Scientific Computing Volume 40, Issue 6

DOI:10.1137/sjoce3.40.6

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© 2018, Society for Industrial and Applied Mathematics.

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Society for Industrial and Applied Mathematics

United States

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Published: 01 January 2018

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Cited By

Deng ZDeng KHu JWen Z(2025)An Augmented Lagrangian Primal-Dual Semismooth Newton Method for Multi-Block Composite OptimizationJournal of Scientific Computing10.1007/s10915-025-02794-4102:3Online publication date: 1-Mar-2025
https://dl.acm.org/doi/10.1007/s10915-025-02794-4
Zhang RLiu XDai Y(2024)IPRSDP: a primal-dual interior-point relaxation algorithm for semidefinite programmingComputational Optimization and Applications10.1007/s10589-024-00558-888:1(1-36)Online publication date: 1-May-2024
https://dl.acm.org/doi/10.1007/s10589-024-00558-8

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