CLASSICAL AND MODERN OPTIMIZATION

類似書籍推薦給您

The quest for the optimal is ubiquitous in nature and human behavior. The field of mathematical optimization has a long history and remains active today, particularly in the development of machine learning. Classical and Modern Optimization presents a self-contained overview of classical and modern ideas and methods in approaching optimization problems. The approach is rich and flexible enough to address smooth and non-smooth, convex and non-convex, finite or infinite-dimensional, static or dynamic situations. The first chapters of the book are devoted to the classical toolbox: topology and functional analysis, differential calculus, convex analysis and necessary conditions for differentiable constrained optimization. The remaining chapters are dedicated to more specialized topics and applications. Valuable to a wide audience, including students in mathematics, engineers, data scientists or economists, Classical and Modern Optimization contains more than 200 exercises to assist with self-study or for anyone teaching a third- or fourth-year optimization class. Sample Chapter(s) Preface Chapter 1: Topological and Functional Analytic Preliminaries Request Inspection Copy Contents: Topological and Functional Analytic Preliminaries: Metric Spaces Normed Vector Spaces Banach Spaces Hilbert Spaces Weak Convergence On the Existence and Generic Uniqueness of Minimizers Exercises Differential Calculus: First-Order Differential Calculus Second-Order Differential Calculus The Inverse Function and Implicit Function Theorems Smooth Functions on ℝd, Regularization, Integration by Parts Exercises Convexity: Hahn–Banach Theorems Convex Sets Convex Functions The Legendre Transform Exercises Optimality Conditions for Differentiable Optimization: Unconstrained Optimization Equality Constraints Equality and Inequality Constraints Exercises Problems Depending on a Parameter: Setting and Examples Continuous Dependence Parameter-Independent Constraints, Envelope Theorems Parameter-Dependent Constraints Discrete-Time Dynamic Programming Exercises Convex Duality and Applications: Generalities Convex Duality with Respect to a Perturbation Applications On the Optimal Transport Problem Exercises Iterative Methods for Convex Minimization: On Newton's Method The Gradient Method The Proximal Point Method Splitting Methods Exercises When Optimization and Data Meet: Principal Component Analysis Minimization for Linear Systems Classification Exercises An Invitation to the Calculus of Variations: Preliminaries On Integral Functionals The Direct Method Euler–Lagrange Equations and Other Necessary Conditions A Focus on the Case d = 1 Exercises Readership: Thought-leaders, executives, industry strategists, research scientists, graduate students, advanced undergraduate students, policy-makers, research funding agencies, private research institutions, government regulators, investors, corporate managers, purchasing agents, and entrepreneurs in the areas of computer science, quantum computing, information theory, neuroscience, and physics.

Fundamentals of Classical and Modern Error-Correcting Codes

類似書籍推薦給您

Using easy-to-follow mathematics, this textbook provides comprehensive coverage of block codes and techniques for reliable communications and data storage. It covers major code designs and constructions from geometric, algebraic, and graph-theoretic points of view, decoding algorithms, error control additive white Gaussian noise (AWGN) and erasure, and dataless recovery. It simplifies a highly mathematical subject to a level that can be understood and applied with a minimum background in mathematics, provides step-by-step explanation of all covered topics, both fundamental and advanced, and includes plenty of practical illustrative examples to assist understanding. Numerous homework problems are included to strengthen student comprehension of new and abstract concepts, and a solutions manual is available online for instructors. Modern developments, including polar codes, are also covered. An essential textbook for senior undergraduates and graduates taking introductory coding courses, students taking advanced full-year graduate coding courses, and professionals working on coding for communications and data storage.