S-SOS: Stochastic Sum-Of-Squares for Parametric Polynomial Optimization
Authors: Licheng Zhu, Mathias Oster, Yuehaw Khoo
NeurIPS 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We present two numerical studies of S-SOS demonstrating its use in applications. The first study (Section 3.1) numerically tests how the optimal values of the SDP Equation (2) p 2s converge to p of the original primal Equation (1) as we increase the degree. The second study (Section 3.2) evaluates the performance of S-SOS for solution extraction and uncertainty quantification in various sensor network localization problems. |
| Researcher Affiliation | Academia | Richard L. Zhu Department of Computational and Applied Mathematics University of Chicago Chicago, IL 60637; Mathias Oster Institute of Geometry and Practical Mathematics RWTH Aachen Aachen, Germany; Yuehaw Khoo Department of Statistics University of Chicago Chicago, IL 60637 |
| Pseudocode | Yes | Algorithm 1 Monte Carlo Point Optimization (MCPO) |
| Open Source Code | Yes | Our code has been provided with our submission and a cleaned-up version will be released publicly once the preprint is public. |
| Open Datasets | No | Once these are specified, we generate a random problem instance by sampling X Uniform( 1, 1)n, A Uniform( 1, 1)d. The paper generates its own data and does not provide public access information for it. |
| Dataset Splits | No | The paper describes generating random problem instances and evaluating performance, but does not specify any train/validation/test dataset splits or their sizes. |
| Hardware Specification | Yes | The SDPs are formulated with the help of Sym Py [34] and solved using CVXPY [35, 36] and Mosek [37] on a server with two Intel Xeon 6130 Gold processors (32 physical cores total) and 256GB of RAM. |
| Software Dependencies | No | The SDPs are formulated with the help of Sym Py [34] and solved using CVXPY [35, 36] and Mosek [37]... Specific version numbers for SymPy and CVXPY are not explicitly provided in the experimental setup description. |
| Experiment Setup | Yes | A given SNL problem type is specified by a spatial dimension ℓ, N sensors, K anchors, a sensing radius r (0, 2ℓ), a noise type (linear), and anchor type (soft penalty or hard equality). |