A Multi-step Inertial Forward-Backward Splitting Method for Non-convex Optimization

Authors: Jingwei Liang, Jalal Fadili, Gabriel Peyré

NeurIPS 2016 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental In this section, we illustrate our results with some numerical experiments carried out on the problems in Example 1.1, 1.2 and 1.3. The convergence profiles of ||xk x || are shown in Figure 1.
Researcher Affiliation Academia Jingwei Liang and Jalal M. Fadili Normandie Univ, ENSICAEN, CNRS, GREYC {Jingwei.Liang,Jalal.Fadili}@greyc.ensicaen.fr Gabriel Peyré CNRS, DMA, ENS Paris Gabriel.Peyre@ens.fr
Pseudocode Yes Algorithm 1: A Multi-step Inertial Forward Backward (Mi FB)
Open Source Code No No explicit statement or link regarding the public release of source code for the described methodology was found.
Open Datasets No For the problem in Example 1.1, we generated y = Axob + ω with m = 48, n = 128, the entries of A are i.i.d. zero-mean and unit variance Gaussian, xob is 8-sparse, and ω Rm is an additive noise with small variance. For Example 1.3, we generated m = 64 training samples with n = 96-dimensional feature space. This indicates the datasets were generated by the authors for their experiments and no public access information is provided.
Dataset Splits No The paper describes how data was generated for the experiments (e.g., 'we generated y = Axob + ω', 'we generated m = 64 training samples') but does not specify explicit train/validation/test dataset splits, percentages, or sample counts for reproducibility.
Hardware Specification No The paper does not provide any specific hardware details (e.g., GPU/CPU models, memory, cloud resources) used for running the experiments.
Software Dependencies No The paper does not list specific software dependencies with version numbers (e.g., 'Python 3.8', 'PyTorch 1.9') that would be required to replicate the experiments.
Experiment Setup Yes For all presented numerical results, 3 different settings were tested: the FB method, with γk 0.3/L, noted as FB ; Mi FB with s = 1, bk = ak a and γk 0.3/L, noted as 1-i FB ; Mi FB with s = 2, bi,k = ai,k ai, i = 0, 1 and γk 0.3/L, noted as 2-i FB . We fix γk 0.3/L for all tests. For the 2 inertial schemes, inertial parameters are first chosen such that (2.3) holds. Then between Thm 2.2 and Bnd (2.4) , Bnd (2.4) shows faster convergence result, since the allowed value of P i Iai of (2.4) is bigger than that of Theorem 2.2.