Game Theory Explained: A Mathematical Introduction with Optimization (1版)
類似書籍推薦給您
【簡介】
This book provides an introduction to the mathematical theory of games using both classical methods and optimization theory. Employing a theorem-proof-example approach, the book emphasizes not only results in game theory, but also how to prove them.Part 1 of the book focuses on classical results in games, beginning with an introduction to probability theory by studying casino games and ending with Nash’s proof of the existence of mixed strategy equilibria in general sum games. On the way, utility theory, game trees and the minimax theorem are covered with several examples. Part 2 introduces optimization theory and the Karush-Kuhn-Tucker conditions and illustrates how games can be rephrased as optimization problems, thus allowing Nash equilibria to be computed. Part 3 focuses on cooperative games. In this unique presentation, Nash bargaining is recast as a multi-criteria optimization problem and the results from linear programming and duality are revived to prove the classic Bondareva-Shapley theorem. Two appendices covering prerequisite materials are provided, and a ＂bonus＂ appendix with an introduction to evolutionary games allows an instructor to swap out some classical material for a modern, self-contained discussion of the replicator dynamics, the author’s particular area of study.
立即查看
Linear and Nonlinear Optimization using Spreadsheets (1版)
類似書籍推薦給您
【簡介】
The use of spreadsheets to obtain solutions to a diverse array of examples offers a reader-friendly way of addressing a topic (optimization) that can sometimes be viewed as intimidating. Many people are readily familiar with spreadsheets and how they work, yet are apt to be unaware of the incredible power of Excel for solving some rather complex optimization problems. A major goal of the book is to sell readers on why it is so important to understand optimization, and a large collection of examples for a wide range of business decision making areas (e.g., production planning and scheduling, workforce planning and scheduling, location and supply chain distribution, location of emergency services, assembly line balancing, vehicle routing, project scheduling, revenue management, advertising, product design, payout schedules, productivity measurement, investment portfolio management, sports league scheduling, ranking models, etc.) affords a practical mechanism for achieving that goal. Another important contribution of the book is that it provides coverage of the mechanics of some common yet sophisticated statistical methods (regression, logistic regression, discriminant analysis, factor analysis, and cluster analysis), which are often opaque to many users of such methods.
【目錄】
Introduction
Optimization Examples in Prescriptive Analytics:
Production Planning
Workforce Planning
Continuous Facility Location
Discrete Facility Location
Routing Problems
Facility Layout
Project Scheduling
Marketing
Finance
Sports
Optimization Examples for Multivariate Statistical Methods Used in Predictive and Descriptive Analytics:
Regression
Logistic Regression
Linear Discriminant Analysis
Factor Analysis
Cluster Analysis
立即查看
An Introduction to Optimization: With Applications to Machine Learning (5版)
類似書籍推薦給您
An Introduction to Optimization
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.
立即查看
華通書坊
