Intro -- Preface -- 1 Preliminaries -- 1.1 Rp Space -- 1.2 Limits of Functions and Continuity -- 1.3 Differentiability -- 1.4 The Riemann Integral -- 2 Nonlinear Analysis Fundamentals -- 2.1 Convex Sets and Cones -- 2.2 Convex Functions -- 2.2.1 General Results -- 2.2.2 Convex Functions of One Variable -- 2.2.3 Inequalities -- 2.3 Banach Fixed Point Principle -- 2.3.1 Contractions and Fixed Points -- 2.3.2 The Case of One Variable Functions -- 2.4 Graves Theorem -- 2.5 Semicontinuous Functions -- 3 The Study of Smooth Optimization Problems -- 3.1 General Optimality Conditions -- 3.2 Functional Restrictions -- 3.2.1 Fritz John Optimality Conditions -- 3.2.2 Karush-Kuhn-Tucker Conditions -- 3.2.3 Qualification Conditions -- 3.3 Second-order Conditions -- 3.4 Motivations for Scientific Computations -- 4 Convex Nonsmooth Optimization -- 4.1 Further Properties and Separation of Convex Sets -- 4.2 The Subdifferential of a Convex Function -- 4.3 Optimality Conditions -- 5 Lipschitz Nonsmooth Optimization -- 5.1 Clarke Generalized Calculus -- 5.1.1 Clarke Subdifferential -- 5.1.2 Clarke Tangent and Normal Cones -- 5.1.3 Optimality Conditions in Lipschitz Optimization -- 5.2 Mordukhovich Generalized Calculus -- 5.2.1 Fr�echet and Mordukhovich Normal Cones -- 5.2.2 Fr�echet and Mordukhovich Subdifferentials -- 5.2.3 The Extremal Principle -- 5.2.4 Calculus Rules -- 5.2.5 Optimality Conditions -- 6 Basic Algorithms -- 6.1 Algorithms for Nonlinear Equations -- 6.1.1 Picard's Algorithm -- 6.1.2 Newton's Method -- 6.2 Algorithms for Optimization Problems -- 6.2.1 The Case of Unconstrained Problems -- 6.2.2 The Case of Constraint Problems -- 6.3 Scientific Calculus Implementations -- 7 Exercises and Problems, and their Solutions -- 7.1 Analysis of Real Functions of One Variable -- 7.2 Nonlinear Analysis -- 7.3 Smooth Optimization -- 7.4 Nonsmooth Optimization.

Bibliography -- List of Notations -- Index.

This book presents the main ideas and techniques in the field of continuous smooth and nonsmooth optimization.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2022. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.