Mathematical Optimization Techniques

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1963.

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 accessible textbook demonstrates how to recognize, simplify, model and solve optimization problems - and apply these principles to new projects.

Optimization is an important tool used in decision science and for the analysis of physical systems used in engineering. One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.

This book presents a structured approach to develop mathematical optimization formulations for several variants of facility layout. The range of layout problems covered includes row layouts, floor layouts, multi-floor layouts, and dynamic layouts. The optimization techniques used to formulate the problems are primarily mixed-integer linear programming, second-order conic programming, and semidefinite programming. The book also covers important practical considerations for solving the formulations. The breadth of approaches presented help the reader to learn how to formulate a variety of problems using mathematical optimization techniques. The book also illustrates the use of layout formulations in selected engineering applications, including manufacturing, building design, automotive, and hospital layout.

The theory of optimization, understood in a broad sense, is the basis of modern applied mathematics, covering a large spectrum of topics from theoretical considerations (structure, stability) to applied operational research and engineering applications. The compiled material of this book puts on display this versatility, by exhibiting the three parallel and complementary components of optimization: theory, algorithms, and practical problems. The book contains an expanded version of three series of lectures delivered by the authors at the CRM in July 2009. The first part is a self-contained course on the general moment problem and its relations with semidefinite programming. The second part is dedicated to the problem of determination of Nash equilibria from an algorithmic viewpoint. The last part presents congestion models for traffic networks and develops modern optimization techniques for finding traffic equilibria based on stochastic optimization and game theory.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1963.

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.