A Review of Linear Programming by G. Hadley
Linear programming is a mathematical technique for optimizing a linear objective function subject to a set of linear constraints. It has applications in various fields, such as operations research, economics, engineering, and management. Linear programming was developed in the 1940s by George Dantzig, John von Neumann, and others.
One of the classic textbooks on linear programming is Linear Programming by G. Hadley, first published in 1962 by Addison-Wesley. The book covers the theory and methods of linear programming, including the simplex method, duality theory, sensitivity analysis, transportation and assignment problems, network flows, integer programming, and nonlinear programming. The book also includes many examples and exercises to illustrate the concepts and techniques.
The book is intended for undergraduate and graduate students of mathematics, engineering, economics, and management who have some background in calculus and matrix algebra. The book is also suitable for researchers and practitioners who want to learn more about linear programming and its applications.
A PDF version of the book is available online at https://archive.org/details/linearprogrammin00hadl. The PDF file has 26 pages and was uploaded in 2012 by the Internet Archive. The file name is "ghadleylinearprogrammingnarosa2002pdf26".
The book is a valuable resource for anyone interested in linear programming and its applications. It provides a comprehensive and rigorous introduction to the subject, as well as a useful reference for advanced topics. The book is written in a clear and concise style, with plenty of examples and exercises to enhance understanding.
The book is organized into 12 chapters and three appendices. The first chapter introduces the basic concepts and terminology of linear programming, such as feasible region, objective function, optimal solution, and extreme point. The second chapter reviews some mathematical background, such as matrices, determinants, inverses, linear independence, rank, and linear equations. The third chapter presents the theory of the simplex method, which is the most widely used algorithm for solving linear programming problems. The fourth chapter discusses the computational aspects of the simplex method, such as pivoting rules, degeneracy, cycling, and artificial variables.
The fifth chapter introduces the concept of duality in linear programming, which relates a given problem to another problem with reversed roles of variables and constraints. The sixth chapter explores the applications of duality theory, such as sensitivity analysis, complementary slackness, and postoptimality analysis. The seventh chapter deals with transportation and assignment problems, which are special types of linear programming problems that arise in logistics and resource allocation. The eighth chapter covers network flow problems, which are also special types of linear programming problems that involve finding the optimal flow of a commodity through a network of nodes and arcs.
The ninth chapter extends the scope of linear programming to integer programming, which involves finding optimal solutions that satisfy additional integrality constraints on some or all of the variables. The tenth chapter discusses some methods for solving integer programming problems, such as branch and bound, cutting planes, and dynamic programming. The eleventh chapter considers nonlinear programming problems, which involve optimizing a nonlinear objective function subject to nonlinear constraints. The twelfth chapter describes some methods for solving nonlinear programming problems, such as gradient methods, penalty methods, and Lagrange multipliers.
The appendices provide some supplementary material on convex sets and functions, linear algebra, and numerical analysis. The book also includes a bibliography and an index. c481cea774