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• W2904112175 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." @default.
• W2904112175 created "2018-12-22" @default.
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• W2904112175 date "2018-01-01" @default.
• W2904112175 modified "2023-10-13" @default.
• W2904112175 title "A SemiSmooth Newton Method for Semidefinite Programs and its Applications in Electronic Structure Calculations" @default.
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• W2904112175 doi "https://doi.org/10.1137/18m1188069" @default.
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