Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..

A Computationally Viable Numerical Gradient-based Technique for Optimal Covering Problems

Authors: Gokul Rajaraman, Debasish Chatterjee

NeurIPS 2025 | Venue PDF | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental This section details the numerical experiments carried out using Algorithm 1. Heuristic observations in (Liu et al., 2024, Section 6) align with our observations: faster convergence is observed when the variance reduction step is omitted (i.e., q = 1, rendering b2 immaterial). We also observe better performance when b1 is increased in response to larger values of n or N. Accordingly, we set q = 1 for all our experiments. For the ease of visualization, we present examples with N = 2 and n < 10 in 4; an illustration with N = 3 is presented in Example D.2 in D. At each point, G is evaluated using the NLP solver BARON (Sahinidis, 1996), known for its global optimization capabilities. To the best of our knowledge, no existing benchmarks or ground truth results are available in the literature, and therefore, our comparisons of computation time and accuracy are with techniques like simulated annealing that do not leverage the Lipschitz continuity of G for outer minimization.
Researcher Affiliation Academia Gokul Rajaraman Department of Mechanical Engineering IIT Bombay Mumbai 400076, India EMAIL Debasish Chatterjee Centre for Systems and Control IIT Bombay Mumbai 400076, India EMAIL
Pseudocode Yes Algorithm 1 grad Opt Net: a numerical gradient-based optimal covering algorithm
Open Source Code No The paper discusses the use of third-party solvers BARON and IPOPT for evaluating G, but it does not provide any explicit statement about making its own implementation code for Algorithm 1 or any other part of its methodology publicly available, nor does it provide a link to a code repository or mention code in supplementary materials.
Open Datasets No The paper does not use any external, publicly available datasets. Instead, it defines the sets M for its numerical experiments mathematically within the text (e.g., solid ellipse in Example 4.1, and asymmetric and nonconvex regions in Example 4.3 and Example D.2).
Dataset Splits No The paper performs numerical experiments on mathematically defined sets. It mentions using "multiple parallel initializations" and "10 restarts" for the algorithm to enhance global convergence efficiency and test robustness. However, this refers to algorithm execution rather than conventional dataset splits (e.g., training/validation/test sets) for external data. No such explicit data split information is provided.
Hardware Specification Yes Table 2 reports the time taken to compute G in Example 4.1 for varying n using BARON in demo mode on an AMD Ryzen 7 4800H 2.90 GHz CPU.
Software Dependencies No The paper mentions using "NLP solver BARON (Sahinidis, 1996)" and "IPOPT" for evaluating G. While these tools are identified, specific version numbers for BARON, IPOPT, or any other programming languages or libraries used for the implementation are not provided.
Experiment Setup Yes The evolution of the objective value for the case n = 4 against the iterations of Algorithm 1, with γ = 0.05, δ = 0.01, b1 = 24, and q = 1 is shown in Fig. 4 featuring 4 restarts. For each n, Algorithm 1 executed with 10 restarts yielded final radius values with relative standard deviation < 1%, indicating excellent robustness.