Derivative-Free Global Minimization in One Dimension: Relaxation, Monte Carlo, and Sampling

2023/08/17 by Alexandra Gomes, Gomes, Alexandra A., Diogo A. Gomes +1
Engineering · Mathematics · Physics and Astronomy · #65K10 #Advanced Optimization Algorithms Research #FOS: Mathematics #Model Reduction and Neural Networks #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.2308.09050

openalex publication_date 2023/08/17 · openalex created_date 2023/08/22 · openalex updated_date 2026/07/28

Abstract

We introduce a derivative-free global optimization algorithm that efficiently computes minima for various classes of one-dimensional functions, including non-convex, and non-smooth functions.This algorithm numerically approximates the gradient flow of a relaxed functional, integrating strategies such as Monte Carlos methods, rejection sampling, and adaptive techniques. These strategies enhance performance in solving a diverse range of optimization problems while significantly reducing the number of required function evaluations compared to established methods. We present a proof of the convergence of the algorithm and illustrate its performance by comprehensive benchmarking. The proposed algorithm offers a substantial potential for real-world models. It is particularly advantageous in situations requiring computationally intensive objective function evaluations.

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