Weighted Trace-Penalty Minimization for Full Configuration Interaction

TL;DR

This paper introduces a new unconstrained optimization model called weighted trace-penalty minimization (WTPM) for solving the eigenvalue problem in Full Configuration Interaction (FCI), with theoretical guarantees and an efficient coordinate descent algorithm.

Contribution

It proposes the WTPM model with theoretical analysis, and develops the WTPM-CD algorithm tailored for sparse FCI matrices, improving computational efficiency.

Findings

WTPM's global minimizers are the desired eigenvectors.

WTPM-CD reduces computational and storage costs.

Numerical experiments confirm effectiveness on large-scale FCI matrices.

Abstract

A novel unconstrained optimization model named weighted trace-penalty minimization (WTPM) is proposed to address the extreme eigenvalue problem arising from the Full Configuration Interaction (FCI) method. Theoretical analysis shows that the global minimizers of the WTPM objective function are the desired eigenvectors, rather than the eigenspace. Analyzing the condition number of the Hessian operator in detail contributes to the determination of a near-optimal weight matrix. With the sparse feature of FCI matrices in mind, the coordinate descent (CD) method is adapted to WTPM and results in WTPM-CD method. The reduction of computational and storage costs in each iteration shows the efficiency of the proposed algorithm. Finally, the numerical experiments demonstrate the capability to address large-scale FCI matrices.