This third edition of the classic textbook in Optimization has been fully revised and updated. It comprehensively covers modern theoretical insights in this crucial computing area, and will be required reading for analysts and operations researchers in a variety of fields. The book connects the purely analytical character of an optimization problem, and the behavior of algorithms used to solve it. Now, the third edition has been completely updated with recent Optimization Methods. The book also has a new co-author, Yinyu Ye of California’s Stanford University, who has written lots of extra material including some on Interior Point Methods.

Nonlinear programming provides an excellent opportunity to explore an interesting variety of pure and solidly applicable mathematics, numerical analysis, and computing. This text develops some of the ideas and techniques involved in the optimization methods using calculus, leading to the study of convexity. This is followed by material on basic numerical methods, least squares, the Karush-Kuhn-Tucker theorem, penalty functions, and Lagrange multipliers. The authors have aimed their presentation at the student who has a working knowledge of matrix algebra and advanced calculus, but has had no previous exposure to optimization.

This book addresses modern nonlinear programming (NLP) concepts and algorithms, especially as they apply to challenging applications in chemical process engineering. The author provides a firm grounding in fundamental NLP properties and algorithms, and relates them to real-world problem classes in process optimization, thus making the material understandable and useful to chemical engineers and experts in mathematical optimization.

COMPREHENSIVE COVERAGE OF NONLINEAR PROGRAMMING THEORY AND ALGORITHMS, THOROUGHLY REVISED AND EXPANDED Nonlinear Programming: Theory and Algorithms—now in an extensively updated Third Edition—addresses the problem of optimizing an objective function in the presence of equality and inequality constraints. Many realistic problems cannot be adequately represented as a linear program owing to the nature of the nonlinearity of the objective function and/or the nonlinearity of any constraints. The Third Edition begins with a general introduction to nonlinear programming with illustrative examples and guidelines for model construction. Concentration on the three major parts of nonlinear programming is provided: Convex analysis with discussion of topological properties of convex sets, separation and support of convex sets, polyhedral sets, extreme points and extreme directions of polyhedral sets, and linear programming Optimality conditions and duality with coverage of the nature, interpretation, and value of the classical Fritz John (FJ) and the Karush-Kuhn-Tucker (KKT) optimality conditions; the interrelationships between various proposed constraint qualifications; and Lagrangian duality and saddle point optimality conditions Algorithms and their convergence, with a presentation of algorithms for solving both unconstrained and constrained nonlinear programming problems Important features of the Third Edition include: New topics such as second interior point methods, nonconvex optimization, nondifferentiable optimization, and more Updated discussion and new applications in each chapter Detailed numerical examples and graphical illustrations Essential coverage of modeling and formulating nonlinear programs Simple numerical problems Advanced theoretical exercises The book is a solid reference for professionals as well as a useful text for students in the fields of operations research, management science, industrial engineering, applied mathematics, and also in engineering disciplines that deal with analytical optimization techniques. The logical and self-contained format uniquely covers nonlinear programming techniques with a great depth of information and an abundance of valuable examples and illustrations that showcase the most current advances in nonlinear problems.

Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern topics such as optimality conditions and numerical methods for problems involving nondifferentiable functions, semidefinite programming, metric regularity and stability theory of set-constrained systems, and sensitivity analysis of optimization problems. Based on a decade's worth of notes the author compiled in successfully teaching the subject, this book will help readers to understand the mathematical foundations of the modern theory and methods of nonlinear optimization and to analyze new problems, develop optimality theory for them, and choose or construct numerical solution methods. It is a must for anyone seriously interested in optimization.

Helps Students Understand Mathematical Programming Principles and Solve Real-World Applications Supplies enough mathematical rigor yet accessible enough for undergraduates Integrating a hands-on learning approach, a strong linear algebra focus, MapleTM software, and real-world applications, Linear and Nonlinear Programming with MapleTM: An Interactive, Applications-Based Approach introduces undergraduate students to the mathematical concepts and principles underlying linear and nonlinear programming. This text fills the gap between management science books lacking mathematical detail and rigor and graduate-level books on mathematical programming. Essential linear algebra tools Throughout the text, topics from a first linear algebra course, such as the invertible matrix theorem, linear independence, transpose properties, and eigenvalues, play a prominent role in the discussion. The book emphasizes partitioned matrices and uses them to describe the simplex algorithm in terms of matrix multiplication. This perspective leads to streamlined approaches for constructing the revised simplex method, developing duality theory, and approaching the process of sensitivity analysis. The book also discusses some intermediate linear algebra topics, including the spectral theorem and matrix norms. Maple enhances conceptual understanding and helps tackle problems Assuming no prior experience with Maple, the author provides a sufficient amount of instruction for students unfamiliar with the software. He also includes a summary of Maple commands as well as Maple worksheets in the text and online. By using Maple’s symbolic computing components, numeric capabilities, graphical versatility, and intuitive programming structures, students will acquire a deep conceptual understanding of major mathematical programming principles, along with the ability to solve moderately sized real-world applications. Hands-on activities that engage students Throughout the book, student understanding is evaluated through "waypoints" that involve basic computations or short questions. Some problems require paper-and-pencil calculations; others involve more lengthy calculations better suited for performing with Maple. Many sections contain exercises that are conceptual in nature and/or involve writing proofs. In addition, six substantial projects in one of the appendices enable students to solve challenging real-world problems.

This book is an introduction to nonlinear programming. It deals with the theoretical foundations and solution methods, beginning with the classical procedures and reaching up to “modern” methods like trust region methods or procedures for nonlinear and global optimization. A comprehensive bibliography including diverse web sites with information about nonlinear programming, in particular software, is presented. Without sacrificing the necessary mathematical rigor, excessive formalisms are avoided. Several examples, exercises with detailed solutions, and applications are provided, making the text adequate for individual studies. The book is written for students from the fields of applied mathematics, engineering, economy, and computation.

This book considers a range of problems in operations research, which are formulated through various mathematical models such as complementarity, variational inequalities, multiobjective optimization, fixed point problems, noncooperative games and inverse optimization. Moreover, the book subsumes all these models under a common structure that allows them to be formulated in a unique format: the Ky Fan inequality. It subsequently focuses on this unifying equilibrium format, providing a comprehensive overview of the main theoretical results and solution algorithms, together with a wealth of applications and numerical examples. Particular emphasis is placed on the role of nonlinear optimization techniques – e.g. convex optimization, nonsmooth calculus, proximal point and descent algorithms – as valuable tools for analyzing and solving Ky Fan inequalities.

Interest in constrained optimization originated with the simple linear pro gramming model since it was practical and perhaps the only computationally tractable model at the time. Constrained linear optimization models were soon adopted in numerous application areas and are perhaps the most widely used mathematical models in operations research and management science at the time of this writing. Modelers have, however, found the assumption of linearity to be overly restrictive in expressing the real-world phenomena and problems in economics, finance, business, communication, engineering design, computational biology, and other areas that frequently demand the use of nonlinear expressions and discrete variables in optimization models. Both of these extensions of the linear programming model are NP-hard, thus representing very challenging problems. On the brighter side, recent advances in algorithmic and computing technology make it possible to re visit these problems with the hope of solving practically relevant problems in reasonable amounts of computational time. Initial attempts at solving nonlinear programs concentrated on the de velopment of local optimization methods guaranteeing globality under the assumption of convexity. On the other hand, the integer programming liter ature has concentrated on the development of methods that ensure global optima. The aim of this book is to marry the advancements in solving nonlinear and integer programming models and to develop new results in the more general framework of mixed-integer nonlinear programs (MINLPs) with the goal of devising practically efficient global optimization algorithms for MINLPs.