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ContentsPreface IIICHAPTER 1Introduction 1.11.1 About Optimization11.2 Classification of Optimizatiou41.3 Preliminaries in Convex Analysis101.4 Exercises15CHAPTER 2Fundamentals of Optimization 172.1 Unconstrained Optimization Problem172.2 What is a Solution?182.2.1 Definitions of Different Solutions182.2.2 Recognizing a Local Minimun202.2.3 Nonsmooth Problems232.3 Overview of Algorithms2523.1 Line Search Strategy262.3.2 Trust Region Strategy302.4Couvergence312.5Scaling322.6Exercises 33CHAPTER 3Line Search Methods353.1Step Length353.1.1 The Wolfe Conditions373.1.2 The Goldstein Conditions403.1.3 Suficient Decrease and Backtracking413.2 Convergence of Line Search Methods423.3 Rate of Convergence443.3.1 Steepest Descent Method443.3.2 Newton's Method163.3.3 Quasi-Newton Methods483.4 Exercises50CHAPTER 4.Trust Regiou Methods514.1Outline of the Trust Reg