Accessible introductory textbook on optimization theory and
methods, with an emphasis on engineering design, featuring MATLAB
exercises and worked examples Fully updated to reflect modern
developments in the field, the Fifth Edition of An Introduction to
Optimization fills the need for an accessible, yet rigorous,
introduction to optimization theory and methods, featuring
innovative coverage and a straightforward approach. The book begins
with a review of basic definitions and notations while also
providing the related fundamental background of linear algebra,
geometry, and calculus. With this foundation, the authors explore
the essential topics of unconstrained optimization problems, linear
programming problems, and nonlinear constrained optimization. In
addition, the book includes an introduction to artificial neural
networks, convex optimization, multi-objective optimization, and
applications of optimization in machine learning. Numerous diagrams
and figures found throughout the book complement the written
presentation of key concepts, and each chapter is followed by
MATLAB® exercises and practice problems that reinforce the
discussed theory and algorithms. The Fifth Edition features a new
chapter on Lagrangian (nonlinear) duality, expanded coverage on
matrix games, projected gradient algorithms, machine learning, and
numerous new exercises at the end of each chapter. An Introduction
to Optimization includes information on: The mathematical
definitions, notations, and relations from linear algebra,
geometry, and calculus used in optimization Optimization
algorithms, covering one-dimensional search, randomized search, and
gradient, Newton, conjugate direction, and quasi-Newton methods
Linear programming methods, covering the simplex algorithm,
interior point methods, and duality Nonlinear constrained
optimization, covering theory and algorithms, convex optimization,
and Lagrangian duality Applications of optimization in machine
learning, including neural network training, classification,
stochastic gradient descent, linear regression, logistic
regression, support vector machines, and clustering. An
Introduction to Optimization is an ideal textbook for a one- or
two-semester senior undergraduate or beginning graduate course in
optimization theory and methods. The text is also of value for
researchers and professionals in mathematics, operations research,
electrical engineering, economics, statistics, and business.
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