A comprehensive introduction to optimization with a focus on practical algorithms for the design of engineering systems. This book offers a comprehensive introduction to optimization with a focus on practical algorithms. The book approaches optimization from an engineering perspective, where the objective is to design a system that optimizes a set of metrics subject to constraints. Readers will learn about computational approaches for a range of challenges, including searching high-dimensional spaces, handling problems where there are multiple competing objectives, and accommodating uncertainty in the metrics. Figures, examples, and exercises convey the intuition behind the mathematical approaches. The text provides concrete implementations in the Julia programming language. Topics covered include derivatives and their generalization to multiple dimensions; local descent and first- and second-order methods that inform local descent; stochastic methods, which introduce randomness into the optimization process; linear constrained optimization, when both the objective function and the constraints are linear; surrogate models, probabilistic surrogate models, and using probabilistic surrogate models to guide optimization; optimization under uncertainty; uncertainty propagation; expression optimization; and multidisciplinary design optimization. Appendixes offer an introduction to the Julia language, test functions for evaluating algorithm performance, and mathematical concepts used in the derivation and analysis of the optimization methods discussed in the text. The book can be used by advanced undergraduates and graduate students in mathematics, statistics, computer science, any engineering field, (including electrical engineering and aerospace engineering), and operations research, and as a reference for professionals.

A broad introduction to algorithms for decision making under uncertainty, introducing the underlying mathematical problem formulations and the algorithms for solving them. Automated decision-making systems or decision-support systems—used in applications that range from aircraft collision avoidance to breast cancer screening—must be designed to account for various sources of uncertainty while carefully balancing multiple objectives. This textbook provides a broad introduction to algorithms for decision making under uncertainty, covering the underlying mathematical problem formulations and the algorithms for solving them. The book first addresses the problem of reasoning about uncertainty and objectives in simple decisions at a single point in time, and then turns to sequential decision problems in stochastic environments where the outcomes of our actions are uncertain. It goes on to address model uncertainty, when we do not start with a known model and must learn how to act through interaction with the environment; state uncertainty, in which we do not know the current state of the environment due to imperfect perceptual information; and decision contexts involving multiple agents. The book focuses primarily on planning and reinforcement learning, although some of the techniques presented draw on elements of supervised learning and optimization. Algorithms are implemented in the Julia programming language. Figures, examples, and exercises convey the intuition behind the various approaches presented.

Choose the Correct Solution Method for Your Optimization ProblemOptimization: Algorithms and Applications presents a variety of solution techniques for optimization problems, emphasizing concepts rather than rigorous mathematical details and proofs. The book covers both gradient and stochastic methods as solution techniques for unconstrained and co

This graduate-level text considers the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; local search heuristics for NP-complete problems, more. 1982 edition.

Rich in publications, the well-established field of discrete optimization nevertheless features relatively few books with ready-to-use computer programs. This book, geared toward upper-level undergraduates and graduate students, addresses that need. In addition, it offers a look at the programs' derivation and performance characteristics. Subjects include linear and integer programming, packing and covering, optimization on networks, and coloring and scheduling. A familiarity with design, analysis, and use of computer algorithms is assumed, along with knowledge of programming in Pascal. The book can be used as a supporting text in discrete optimization courses or as a software handbook, with twenty-six programs that execute the most common algorithms in each topic area. Each chapter is self-contained, allowing readers to browse at will.

Optimization is a key concept in mathematics, computer science, and operations research, and is essential to the modeling of any system, playing an integral role in computer-aided design. Fundamentals of Optimization Techniques with Algorithms presents a complete package of various traditional and advanced optimization techniques along with a variety of example problems, algorithms and MATLAB© code optimization techniques, for linear and nonlinear single variable and multivariable models, as well as multi-objective and advanced optimization techniques. It presents both theoretical and numerical perspectives in a clear and approachable way. In order to help the reader apply optimization techniques in practice, the book details program codes and computer-aided designs in relation to real-world problems. Ten chapters cover, an introduction to optimization; linear programming; single variable nonlinear optimization; multivariable unconstrained nonlinear optimization; multivariable constrained nonlinear optimization; geometric programming; dynamic programming; integer programming; multi-objective optimization; and nature-inspired optimization. This book provides accessible coverage of optimization techniques, and helps the reader to apply them in practice. Presents optimization techniques clearly, including worked-out examples, from traditional to advanced Maps out the relations between optimization and other mathematical topics and disciplines Provides systematic coverage of algorithms to facilitate computer coding Gives MATLAB© codes in relation to optimization techniques and their use in computer-aided design Presents nature-inspired optimization techniques including genetic algorithms and artificial neural networks

In the last few years, Algorithms for Convex Optimization have revolutionized algorithm design, both for discrete and continuous optimization problems. For problems like maximum flow, maximum matching, and submodular function minimization, the fastest algorithms involve essential methods such as gradient descent, mirror descent, interior point methods, and ellipsoid methods. The goal of this self-contained book is to enable researchers and professionals in computer science, data science, and machine learning to gain an in-depth understanding of these algorithms. The text emphasizes how to derive key algorithms for convex optimization from first principles and how to establish precise running time bounds. This modern text explains the success of these algorithms in problems of discrete optimization, as well as how these methods have significantly pushed the state of the art of convex optimization itself.