Introduction to derivativefree optimization
by Andrew R. Conn , Katya Scheinberg , Luis N. Vicente

Persian Title: آشنايي با مشتق رایگان بهینه سازی

Summary and Info
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 derivativefree 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 DerivativeFree 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 modelbased approaches. It contains a comprehensive description of the sampling and modeling tools needed for derivativefree optimization; these tools allow the reader to better understand the convergent properties of the algorithms and identify their differences and similarities. Introduction to DerivativeFree Optimization also contains analysis of convergence for modified Nelder Mead and implicitfiltering methods, as well as for modelbased methods such as wedge methods and methods based on minimumnorm Frobenius models. Audience: The book is intended for anyone interested in using optimization on problems where derivatives are difficult or impossible to obtain. Such audiences include chemical, mechanical, aeronautical, and electrical engineers, as well as economists, statisticians, operations researchers, management scientists, biological and medical researchers, and computer scientists. It is also appropriate for use in an advanced undergraduate or early graduatelevel course on optimization for students having a background in calculus, linear algebra, and numerical analysis. Contents: Preface; Chapter 1: Introduction; Part I: Sampling and modeling; Chapter 2: Sampling and linear models; Chapter 3: Interpolating nonlinear models; Chapter 4: Regression nonlinear models; Chapter 5: Underdetermined interpolating models; Chapter 6: Ensuring well poisedness and suitable derivativefree models; Part II: Frameworks and algorithms; Chapter 7: Directional directsearch methods; Chapter 8: Simplicial directsearch methods; Chapter 9: Linesearch methods based on simplex derivatives; Chapter 10: Trustregion methods based on derivativefree models; Chapter 11: Trustregion interpolationbased methods; Part III: Review of other topics; Chapter 12: Review of surrogate model management; Chapter 13: Review of constrained and other extensions to derivativefree optimization; Appendix: Software for derivativefree optimization; Bibliography; Index.
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