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14.09.15 - The textbook "Optimization: principles and algorithms" by Michel Bierlaire is an extended version in English of the book Bierlaire (2006) "Introduction à l'optimisation différentiable", PPUR. Completely revised, with 7 new chapters and a companion website with the code of all algorithms, the new book is designed to be a pedagogical support to teach the main principles of optimization.

Optimization algorithms are important tools for engineers, but difficult to use. In fact, none of them is universal, and a good understanding of the different methods is necessary in order to identify the most appropriate one in the context of specific applications. Designed to teach undergraduate engineering students about optimization, this book also provides the professionals employing optimization methods with significant elements to identify the methods that are appropriate for their applications, and to understand the possible failures of certain methods on their problem. The content is meant to be formal, in the sense that the results presented are proven in detail, and all described algorithms have been implemented and tested by the author. In addition, the many numeric and graphic illustrations constitute a significant base for understanding the methods. The book features eight parts. The first part focuses on the formulation and the analysis of the optimization problem. It describes the modeling process that leads to an optimization problem, as well as the transformations of the problem into an equivalent formulation. The properties of the problem and corresponding hypotheses are discussed independently of the algorithms. Subsequently, the optimality conditions, the theoretical foundations that are essential for properly mastering the algorithms, are analyzed in detail in Part II. Before explaining the methods for unconstrained continuous optimization in Part IV, algorithms for solving systems of non linear equations, based on Newton's method, are described in Part III. The algorithms for constrained continuous optimization constitute the fifth part. Part VI addresses optimization problems based on network structures, elaborating more specifically on the shortest path problem, and the maximum flow problem. Discrete optimization problems, where the variables are constrained to take integer values, are introduced in Part VII, where both exact methods and heuristics are presented. The last part is an appendix containing the definitions and theoretical results used in the book.

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