Introduction to Derivative-Free Optimization (Mps-siam Series on Optimization)

The Absence Of Derivatives, Often Combined With The Presence Of Noise Or Lack Of Smoothness, Is A Major Challenge For Optimisation. 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 Optimisation Problems. Introduction -- Sampling And Linear Models -- Interpolating Nonlinear Models -- Regression Nonlinear Models -- Underdetermined Interpolating Models -- Ensuring Well Poisedness And Suitable Derivative-free Models -- Directional Direct-search Methods -- Simplicial Direct-search Methods -- Line-search Methods Based On Simplex Derivatives -- Trust-region Methods Based On Derivative-free Models -- Trust-region Interpolation-based Methods -- Review Of Surrogate Model Management -- Review Of Constrained And Other Extensions To Derivative-free Optimization. Andrew R. Conn, Katya Scheinberg, Luis N. Vicente. Includes Bibliographical References (p. 255-270) And Index. 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. "This book is the first contemporary comprehensive treatment of optimization without derivatives, and it covers most of the relevant classes of algorithms from direct-search to model-based approaches. - It 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 graduate-level course on optimization for students having a background in calculus, linear algebra, and numerical analysis."--Jacket