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.

翻译：针对全组态相互作用（FCI）方法中的极端特征值问题，本文提出了一种名为加权迹罚最小化（WTPM）的新型无约束优化模型。理论分析表明，WTPM目标函数的全局最小值点对应的是期望的特征向量，而非特征子空间。通过详细分析Hessian算子的条件数，有助于确定近乎最优的权重矩阵。结合FCI矩阵的稀疏特性，将坐标下降（CD）方法应用于WTPM，形成了WTPM-CD方法。每轮迭代中计算与存储成本的降低验证了该算法的有效性。最后，数值实验表明该方法能够处理大规模FCI矩阵。