The Convergence and Error Analysis of Coordinate Descent Methods with Compression for Full Configuration Interaction

2026/07/27 by Yingzhou Li, Qiang Wu
#math.NA #cs.NA #math.OC

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Abstract

We study the effect of compression in Coordinate Descent Full Configuration Interaction (CDFCI) within an unconstrained optimization formulation of the full configuration interaction ground-state problem. Under suitable local assumptions, we prove that the compressed iteration converges linearly to the solution of an associated restricted problem. We also characterize the convergence point of the compressed algorithm. Under an additional exponential decay assumption on the target eigenvector, we show that the resulting eigenvalue error is of order τ², where τ denotes the compression threshold. Numerical results support the analysis.

Citations

• Global Convergence of Adaptive Sensing for Principal Eigenvector Estimation
• Parallel Multi-Coordinate Descent Methods for Full Configuration Interaction
• Coordinate Descent Full Configuration Interaction for Excited States
• Analysis of Truncated Orthogonal Iteration for Sparse Eigenvector Problems
• Coordinate Descent Algorithms
• Truncated Power Method for Sparse Eigenvalue Problems
• Iteration Complexity of Randomized Block-Coordinate Descent Methods for\n Minimizing a Composite Function
• A direct formulation for sparse PCA using semidefinite programming

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