This book provides a comprehensive introduction to nonlinear programming, featuring a broad range of applications and solution methods in the field of continuous optimization. It begins with a summary of classical results on unconstrained optimization, followed by a wealth of applications from a diverse mix of fields, e.g. location analysis, traffic planning, and water quality management, to name but a few. In turn, the book presents a formal description of optimality conditions, followed by an in-depth discussion of the main solution techniques. Each method is formally described, and then fully solved using a numerical example.

Built on the framework of the successful first edition, this book serves as a modern introduction to the field of optimization. The author’s objective is to provide the foundations of theory and algorithms of nonlinear optimization as well as to present a variety of applications from diverse areas of applied sciences. Introduction to Nonlinear Optimization gradually yet rigorously builds connections between theory, algorithms, applications, and actual implementation. The book contains several topics not typically included in optimization books, such as optimality conditions in sparsity constrained optimization, hidden convexity, and total least squares. Readers will discover a wide array of applications such as circle fitting, Chebyshev center, the Fermat–Weber problem, denoising, clustering, total least squares, and orthogonal regression. These applications are studied both theoretically and algorithmically, illustrating concepts such as duality. Python and MATLAB programs are used to show how the theory can be implemented. The extremely popular CVX toolbox (MATLAB) and CVXPY module (Python) are described and used. More than 250 theoretical, algorithmic, and numerical exercises enhance the reader's understanding of the topics. (More than 70 of the exercises provide detailed solutions, and many others are provided with final answers.) The theoretical and algorithmic topics are illustrated by Python and MATLAB examples. This book is intended for graduate or advanced undergraduate students in mathematics, computer science, electrical engineering, and potentially other engineering disciplines.

This textbook provides students with fundamentals and advanced concepts in optimization and operations research. It gives an overview of the historical perspective of operations research and explains its principal characteristics, tools, and applications. The wide range of topics covered includes convex and concave functions, simplex methods, post optimality analysis of linear programming problems, constrained and unconstrained optimization, game theory, queueing theory, and related topics. The text also elaborates on project management, including the importance of critical path analysis, PERT and CPM techniques. This textbook is ideal for any discipline with one or more courses in optimization and operations research; it may also provide a solid reference for researchers and practitioners in operations research.

Optimization is the act of obtaining the "best" result under given circumstances. In design, construction, and maintenance of any engineering system, engineers must make technological and managerial decisions to minimize either the effort or cost required or to maximize benefits. There is no single method available for solving all optimization problems efficiently. Several optimization methods have been developed for different types of problems. The optimum-seeking methods are mathematical programming techniques (specifically, nonlinear programming techniques). Nonlinear Optimization: Models and Applications presents the concepts in several ways to foster understanding. Geometric interpretation: is used to re-enforce the concepts and to foster understanding of the mathematical procedures. The student sees that many problems can be analyzed, and approximate solutions found before analytical solutions techniques are applied. Numerical approximations: early on, the student is exposed to numerical techniques. These numerical procedures are algorithmic and iterative. Worksheets are provided in Excel, MATLAB®, and MapleTM to facilitate the procedure. Algorithms: all algorithms are provided with a step-by-step format. Examples follow the summary to illustrate its use and application. Nonlinear Optimization: Models and Applications: Emphasizes process and interpretation throughout Presents a general classification of optimization problems Addresses situations that lead to models illustrating many types of optimization problems Emphasizes model formulations Addresses a special class of problems that can be solved using only elementary calculus Emphasizes model solution and model sensitivity analysis About the author: William P. Fox is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School. He received his Ph.D. at Clemson University and has taught at the United States Military Academy and at Francis Marion University where he was the chair of mathematics. He has written many publications, including over 20 books and over 150 journal articles. Currently, he is an adjunct professor in the Department of Mathematics at the College of William and Mary. He is the emeritus director of both the High School Mathematical Contest in Modeling and the Mathematical Contest in Modeling.

This textbook provides a thorough introduction to the field of learning from experimental data and soft computing. Support vector machines (SVM) and neural networks (NN) are the mathematical structures, or models, that underlie learning, while fuzzy logic systems (FLS) enable us to embed structured human knowledge into workable algorithms. The book assumes that it is not only useful, but necessary, to treat SVM, NN, and FLS as parts of a connected whole. Throughout, the theory and algorithms are illustrated by practical examples, as well as by problem sets and simulated experiments. This approach enables the reader to develop SVM, NN, and FLS in addition to understanding them. The book also presents three case studies: on NN-based control, financial time series analysis, and computer graphics. A solutions manual and all of the MATLAB programs needed for the simulated experiments are available.

This text provides the undergraduate chemical engineering student with the necessary tools for problem solving in chemical or bio-engineering processes. In a friendly, simple, and unified framework, the exposition aptly balances theory and practice. It uses minimal mathematical concepts, terms, algorithms, and describes the main aspects of chemical process optimization using MATLAB and GAMS. Numerous examples and case studies are designed for students to understand basic principles of each optimization method and elicit the immediate discovery of practical applications. Problem sets are directly tied to real-world situations most commonly encountered in chemical engineering applications. Chapters are structured with handy learning summaries, terms and concepts, and problem sets, and individually reinforce the basics of particular optimization methods. Additionally, the wide breadth of topics that may be encountered in courses such as Chemical Process Optimization, Chemical Process Engineering, Optimization of Chemical Processes, are covered in this accessible text. The book provides formal introductions to MATLAB, GAMS, and a revisit to pertinent aspects of undergraduate calculus. While created for coursework, this text is also suitable for independent study. A full solutions manual is available to instructors who adopt the text for their course.

The only book offering solved exercises for integer and combinatorial optimization, this book contains 102 classroom tested problems of varying scope and difficulty chosen from a plethora of topics and applications. It has an associated website containing additional problems, lecture notes, and suggested readings. Topics covered include modeling capabilities of integer variables, the Branch-and-Bound method, cutting planes, network optimization models, shortest path problems, optimum tree problems, maximal cardinality matching problems, matching-covering duality, symmetric and asymmetric TSP, 2-matching and 1-tree relaxations, VRP formulations, and dynamic programming. Problems and Solutions for Integer and Combinatorial Optimization: Building Skills in Discrete Optimization is meant for undergraduate and beginning graduate students in mathematics, computer science, and engineering to use for self-study and for instructors to use in conjunction with other course material and when teaching courses in discrete optimization.

This volume provides a general overview on the state-of-the-art and future developments in automation and control. The application of systems and control in all areas is covered, from the social and cultural effects of control, to control in mineral and metal processing. This volume will be an invaluable source of information to all those interested in the areas of automation and control.