Introduction to Derivative–Free Optimization

The absence of derivatives, often combined with the presence of noise or lack of smoothness, is a major challenge for optimization. This book explains how sampling and model techniques are used in derivative-free methods and how these methods are designed to efficiently and rigorously solve optimization problems. Although readily accessible to readers with a modest background in computational mathematics, it is also intended to be of interest to researchers in the field. Introduction to Derivative-Free Optimization is the first contemporary comprehensive treatment of optimization without derivatives. This book covers most of the relevant classes of algorithms from direct search to model-based approaches. It contains a comprehensive description of the sampling and modeling tools needed for derivative-free optimization; these tools allow the reader to better analyze the convergent properties of the algorithms and identify their differences and similarities.

Preface; 1. Introduction; Part I. Sampling and Modeling: 2. Sampling and linear models; 3. Interpolating nonlinear models; 4. Regression nonlinear models; 5. Underdetermined interpolating models; 6. Ensuring well poisedness and suitable derivative-free models; Part II. Frameworks and Algorithms: 7. Directional direct-search methods; 8. Simplicial direct-search methods; 9. Line-search methods based on simplex derivatives; 10. Trust-region methods based on derivative-free models; 11. Trust-region interpolation-based methods; Part III. Review of Other Topics: 12. Review of surrogate model management; 13. Review of constrained and other extensions to derivative-free optimization; Appendix: software for derivative-free optimization; Bibliography; Index.

The first contemporary comprehensive treatment of optimization without derivatives. This text explains how sampling and model techniques are used in derivative-free methods and how they are designed to solve optimization problems. It is designed to be readily accessible to both researchers and those with a modest background in computational mathematics.