Proposal of new algorithms for the electronic structure calculation based on the reduced-density-matrix method

量子化学中最基本的问题之一是电子结构计算问题。利用约化密度矩阵方法，我们可以得到一个半定规划问题的近似解。这种方法在理论和数值方面都是非常有吸引力的。然而，与通常的方法相比，它的计算时间非常慢，不能用于大规模问题。我们成功地用并行原-对偶内点法高精度地求解了大规模半定规划问题。这个问题被认为是迄今为止解决的最大的半定规划问题之一。

One of the most basic problems in quantum chemistry is the electronic structure calculation problem. Using the reduced-density-matrix method, we can obtain an approximate solution solving a convex problem called semidefinite programming problem. This approach is known to be very attractive both in theoretical and numerical aspects. However, its computational time is extremely slow compared to the usual methods and it cannot be used to large-scale problems. We succeed to solve the large-scale semidefinite programming problem with high accuracy using a parallel primal-dual interior-point method. This problem is considered one of the largest semidefinite programming problems solved so far.