Introduction to Interpolation-Based Optimization
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915533972045824 |
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| author | Roberts, Lindon |
| author_facet | Roberts, Lindon |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04473 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Introduction to Interpolation-Based Optimization Roberts, Lindon Optimization and Control 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. |
| title | Introduction to Interpolation-Based Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2510.04473 |