{"ID":2859683,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.04473","arxiv_id":"2510.04473","title":"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.","short_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 fo...","url_abs":"https://arxiv.org/abs/2510.04473","url_pdf":"https://arxiv.org/pdf/2510.04473v1","authors":"[\"Lindon Roberts\"]","published":"2025-10-06T04:12:45Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}