Introduction to Interpolation-Based Optimization
Abstract
The field of derivative-free optimization (DFO) studies algorithms for nonlinear optimization that do not rely on the availability of gradient or Hessian information. It is primarily designed for settings when functions are black-box, expensive to evaluate and/or noisy. A widely used and studied class of DFO methods for local optimization is interpolation-based optimization (IBO), also called model-based DFO, where the general principles from derivative-based nonlinear optimization algorithms are followed, but local Taylor-type approximations are replaced with alternative local models constructed by interpolation. This document provides an overview of the basic algorithms and analysis for IBO, covering worst-case complexity, approximation theory for polynomial interpolation models, and extensions to constrained and noisy problems.
Cite
@article{arxiv.2510.04473,
title = {Introduction to Interpolation-Based Optimization},
author = {Lindon Roberts},
journal= {arXiv preprint arXiv:2510.04473},
year = {2025}
}