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Description of  An Introduction to Nonlinear Optimization Theory

311042603X pdf The goal of this book is to present the main ideas and techniques in the field of continuous smooth and nonsmooth optimization. Starting with the case of differentiable data and the classical results on constrained optimization problems, and continuing with the topic of nonsmooth objects involved in optimization theory, the book concentrates on both theoretical and practical aspects of this field. This book prepares those who are engaged in research by giving repeated insights into ideas that are subsequently dealt with and illustrated in detail. This book aims to provide a thorough introduction to smooth and nonsmooth (convex and nonconvex) optimization theory on finite dimensional normed vector spaces (Rp spaces with p ? N \ {0}). We present several important achievements of nonlinear analysis that motivate optimization problems and offer deeper insights into the further developments. Many of the results in this book hold in more general normed vector spaces, but the fundamental ideas of the theory are similar in every setting. We chose the framework of finite dimensional vector spaces since it offers the possibility to simplify some of the proofs and permits an intuitive understanding of the main ideas.