Practical Mathematical Optimization: Basic Optimization Theory and Gradient-Based Algorithms (Springer Optimization and Its Applications Book 133)

This book presents basic optimization principles and gradient-based algorithms to a general audience, in a brief and easy-to-read form. It enables professionals to apply optimization theory to engineering, physics, chemistry, or business economics. This textbook presents a wide range of tools for a course in mathematical optimization for upper undergraduate and graduate students in mathematics, engineering, computer science, and other applied sciences. Basic optimization principles are presented with emphasis on gradient-based numerical optimization strategies and algorithms for solving both smooth and noisy discontinuous optimization problems. Attention is also paid to the difficulties of expense of function evaluations and the existence of multiple minima that often unnecessarily inhibit the use of gradient-based methods. This second edition addresses further advancements of gradient-only optimization strategies to handle discontinuities in objective functions. New chapters discuss the construction of surrogate models as well as new gradient-only solution strategies and numerical optimization using Python. A special Python module is electronically available (via springerlink) that makes the new algorithms featured in the text easily accessible and directly applicable. Numerical examples and exercises are included to encourage senior- to graduate-level students to plan, execute, and reflect on numerical investigations. By gaining a deep understanding of the conceptual material presented, students, scientists, and engineers will be able to develop systematic and scientific numerical investigative skills.-- Provided by publisher This book presents basic optimization principles and gradient-based algorithms to a general audience in a brief and easy-to-read form, without neglecting rigor. The text is structured to let professionals apply optimization theory and algorithms to their own practical fields of interest, such as engineering, physics, chemistry, or business economics. Most importantly, due attention is paid to the difficulties - such as noise, discontinuities, expense of function evaluations, and the existence of multiple minima - that often unnecessarily inhibit the use of gradient-based methods. In a separate chapter on new gradient-based methods developed by the author and his coworkers, it is shown how these difficulties may be overcome without losing the desirable features of classical gradient-based methods. The text includes theorems of special interest, and many worked examples.