Approximate Secular Equations for the Cubic Regularization Subproblem

Authors: Yihang Gao, Man-Chung Yue, Michael Ng

NeurIPS 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental Numerical experiments with synthetic and real data-sets are conducted to investigate the practical performance of the proposed CRS solver. Experimental results show that the proposed solver outperforms two state-of-the-art methods.
Researcher Affiliation Academia Yihang Gao Department of Mathematics The University of Hong Kong Pokfulam, Hong Kong gaoyh@connect.hku.hk Man-Chung Yue Musketeers Foundation Institute of Data Science The University of Hong Kong Pokfulam, Hong Kong mcyue@hku.hk Michael K. Ng Department of Mathematics The University of Hong Kong Pokfulam, Hong Kong mng@maths.hku.hk
Pseudocode Yes The resulting CRS solver, namely the approximate secular equation method (ASEM), is summarized as follows: Step 1: obtaining the partial eigen information {λ1, , λm} and {v1, , vm} of A. Step 2: solving the secular equation (5) with µ defined in (7) or (10); we get σ . Step 3: iteratively solving the linear system (A + σ I)x + b = 0. Output: the solution x.
Open Source Code No Our results are reproducible and we will share our code on github later.
Open Datasets Yes Numerical experiments with synthetic and real data-sets are conducted to investigate the practical performance of the proposed CRS solver. Experimental results show that the proposed solver outperforms two state-of-the-art methods.
Dataset Splits No The paper describes experiments and reports performance metrics but does not specify training, validation, or testing dataset splits.
Hardware Specification Yes All experiments were run on a Macbook Pro M1 laptop.
Software Dependencies No To the best of our knowledge, the mentioned iterative method for partial eigen information is supported in many softwares, e.g., Matlab (eigs function) and Python (Scipy package) etc. (No specific version numbers are provided for these software dependencies).
Experiment Setup Yes The vector b is proportional to [1, , 1]T with kbk = 0.1. The remaining parameters are n = 5 103 and = 0.1.