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Linear Programming
The book provides a broad introduction to both the theory and the application of optimization with a special emphasis on the elegance, importance, and usefulness of the parametric self-dual simplex method. The book assumes that a problem in “standard form,” is a problem with inequality constraints and nonnegative variables. The main new innovation to the book is the use of clickable links to the (newly updated) online app to help students do the trivial but tedious arithmetic when solving optimization problems.The latest edition now includes: a discussion of modern Machine Learning applications, as motivational material; a section explaining Gomory Cuts and an application of integer programming to solve Sudoku problems. Readers will discover a host of practical business applications as well as non-business applications. Topics are clearly developed with many numerical examples worked out in detail. Specific examples and concrete algorithms precede more abstract topics. With its focus on solving practical problems, the book features free C programs to implement the major algorithms covered, including the two-phase simplex method, the primal-dual simplex method, the path-following interior-point method, and and the homogeneous self-dual method. In addition, the author provides online tools that illustrate various pivot rules and variants of the simplex method, both for linear programming and for network flows. These C programs and online pivot tools can be found on the book's website. The website also includes new online instructional tools and exercises.
R 4,159.06
R 5,826.00
R 275.00
Linear Programming and Extensions
In real-world problems related to finance, business, and management, mathematicians and economists frequently encounter optimization problems. In this classic book, George Dantzig looks at a wealth of examples and develops linear programming methods for their solutions. He begins by introducing the basic theory of linear inequalities and describes the powerful simplex method used to solve them. Treatments of the price concept, the transportation problem, and matrix methods are also given, and key mathematical concepts such as the properties of convex sets and linear vector spaces are covered. George Dantzig is properly acclaimed as the "father of linear programming." Linear programming is a mathematical technique used to optimize a situation. It can be used to minimize traffic congestion or to maximize the scheduling of airline flights. He formulated its basic theoretical model and discovered its underlying computational algorithm, the "simplex method," in a pathbreaking memorandum published by the United States Air Force in early 1948.Linear Programming and Extensions provides an extraordinary account of the subsequent development of his subject, including research in mathematical theory, computation, economic analysis, and applications to industrial problems. Dantzig first achieved success as a statistics graduate student at the University of California, Berkeley. One day he arrived for a class after it had begun, and assumed the two problems on the board were assigned for homework. When he handed in the solutions, he apologized to his professor, Jerzy Neyman, for their being late but explained that he had found the problems harder than usual. About six weeks later, Neyman excitedly told Dantzig, "I've just written an introduction to one of your papers. Read it so I can send it out right away for publication." Dantzig had no idea what he was talking about. He later learned that the "homework" problems had in fact been two famous unsolved problems in statistics.
R 5,627.27
Solutions Manual to accompany Nonlinear Programming
As the Solutions Manual, this book is meant to accompany the main title, Nonlinear Programming: Theory and Algorithms, Third Edition. This book presents recent developments of key topics in nonlinear programming (NLP) using a logical and self-contained format. The volume is divided into three sections: convex analysis, optimality conditions, and dual computational techniques. Precise statements of algortihms are given along with convergence analysis. Each chapter contains detailed numerical examples, graphical illustrations, and numerous exercises to aid readers in understanding the concepts and methods discussed.
R 1,088.00
