Local Linear Convergence of Forward--Backward under Partial Smoothness
Authors: Jingwei Liang, Jalal Fadili, Gabriel Peyré
NeurIPS 2014 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Several experimental results on some of the problems discussed above are provided to support our theoretical findings. 4 Numerical experiments In this section, we describe some examples to demonstrate the applicability of our results. More precisely, we consider solving min x Rn 1 2||y Ax||2 + λJ(x) (4.1) |
| Researcher Affiliation | Academia | Jingwei Liang and Jalal M. Fadili GREYC, CNRS-ENSICAEN-Univ. Caen {Jingwei.Liang,Jalal.Fadili}@greyc.ensicaen.fr Gabriel Peyré CEREMADE, CNRS-Univ. Paris-Dauphine Gabriel.Peyre@ceremade.dauphine.fr |
| Pseudocode | No | The paper describes the Forward Backward (FB) splitting algorithm using a mathematical update rule (1.2) but does not provide it in a structured pseudocode or algorithm block format. |
| Open Source Code | No | The paper does not provide any concrete access to source code for the methodology described. |
| Open Datasets | No | The paper describes generating synthetic data for its experiments (e.g., 'A Rm n is generated uniformly at random from the Gaussian ensemble', 'x0 is 8-sparse', 'rank(x0) = 5') rather than using publicly available datasets with concrete access information. |
| Dataset Splits | No | The paper describes the experimental settings for various problems but does not provide specific dataset split information (e.g., percentages or counts for training, validation, or test sets). |
| Hardware Specification | No | The paper does not provide any specific hardware details used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific ancillary software details with version numbers. |
| Experiment Setup | Yes | The tested experimental settings are (a) ℓ1-norm m = 48 and n = 128, x0 is 8-sparse; (b) Total Variation m = 48 and n = 128, (DDIFx0) is 8-sparse; (c) ℓ∞-norm m = 123 and n = 128, x0 has 10 saturating entries; (d) ℓ1 ℓ2-norm m = 48 and n = 128, x0 has 2 non-zero blocks of size 4; (e) Nuclear norm m = 1425 and n = 2500, x0 R50 50 and rank(x0) = 5. The number of measurements is chosen sufficiently large, δ small enough and λ of the order of δ so that [27, Theorem 1] applies, yielding that the minimizer of (4.1) is unique and verifies the non-degeneracy and restricted strong convexity assumptions (3.1)-(3.2). |