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. |