Semidefinite programming formulation of linear-scaling electronic structure theories

Linear Scaling Electronic Structure Methods

Methods exhibiting linear scaling with respect to the size of the system, so called O(N) methods, are an essential tool for the calculation of the electronic structure of large systems containing many atoms. They are based on algorithms which take advantage of the decay properties of the density matrix. In this article the physical decay properties of the density matrix will first be studied fo...

Linear Scaling Electronic Structure Methods

Graph-based linear scaling electronic structure theory.

We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials, including challenging systems such as biomolecules. The methodology combines well-controlled accuracy, low computational cost, and natural low-communication paral...

A Recurrent Neural Network Model for Solving Linear Semidefinite Programming

In this paper we solve a wide rang of Semidefinite Programming (SDP) Problem by using Recurrent Neural Networks (RNNs). SDP is an important numerical tool for analysis and synthesis in systems and control theory. First we reformulate the problem to a linear programming problem, second we reformulate it to a first order system of ordinary differential equations. Then a recurrent neural network...

Affine scaling algorithm fails for semidefinite programming

In this paper, we introduce an aane scaling algorithm for semideenite programming, and give an example of a semideenite program such that the aane scaling algorithm converges to a non-optimal point. Both our program and its dual have interior feasible solutions, and unique optimal solutions which satisfy strict complementarity, and they are nondegenerate everywhere. Abbreviated Title: AAne scal...