Chapter 7: Optimization algorithms
Abstract
The deterministic inverse problems considered in the present book are formulated as optimization problems over function spaces. Once discretized, we need to deploy an optimization algorithm to solve such problems. We focus primarily on Newton-type methods for such optimization problems. Accordingly, the aim of this chapter is to cover the requisite background regarding line search methods, and Newton’s method along with some of its popular variants. Throughout, we consider optimization problems of the form \begin{equation}\min_{x \in \mathbb{R}^n} J(x),\end{equation} (7.1)where \(J: \mathbb{R}^{n} \rightarrow \mathbb{R}\) is an objective function.
Fields of Study & Subjects
Advanced Optimization Algorithms Research
Numerical methods in inverse problems
Optimization and Variational Analysis
Publication details
- Journal / source
- Society for Industrial and Applied Mathematics eBooks
- Pages
- 83–94
- Publication date
- 27 February 2026
- Language
- EN
- Document type
- Book chapter