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.

Semidefinite and conic optimization is a major and thriving research area within the optimization community. Although semidefinite optimization has been studied (under different names) since at least the 1940s, its importance grew immensely during the 1990s after polynomial-time interior-point methods for linear optimization were extended to solve semidefinite optimization problems. Since the beginning of the 21st century, not only has research into semidefinite and conic optimization continued unabated, but also a fruitful interaction has developed with algebraic geometry through the close connections between semidefinite matrices and polynomial optimization. This has brought about important new results and led to an even higher level of research activity. This Handbook on Semidefinite, Conic and Polynomial Optimization provides the reader with a snapshot of the state-of-the-art in the growing and mutually enriching areas of semidefinite optimization, conic optimization, and polynomial optimization. It contains a compendium of the recent research activity that has taken place in these thrilling areas, and will appeal to doctoral students, young graduates, and experienced researchers alike. The Handbook's thirty-one chapters are organized into four parts: Theory, covering significant theoretical developments as well as the interactions between conic optimization and polynomial optimization; Algorithms, documenting the directions of current algorithmic development; Software, providing an overview of the state-of-the-art; Applications, dealing with the application areas where semidefinite and conic optimization has made a significant impact in recent years.

Semidefinite and conic optimization is a major and thriving research area within the optimization community. Although semidefinite optimization has been studied (under different names) since at least the 1940s, its importance grew immensely during the 1990s after polynomial-time interior-point methods for linear optimization were extended to solve semidefinite optimization problems.

Since the beginning of the 21st century, not only has research into semidefinite and conic optimization continued unabated, but also a fruitful interaction has developed with algebraic geometry through the close connections between semidefinite matrices and polynomial optimization. This has brought about important new results and led to an even higher level of research activity.

This "Handbook on Semidefinite, Conic and Polynomial Optimization "provides the reader with a snapshot of the state-of-the-art in the growing and mutually enriching areas of semidefinite optimization, conic optimization, and polynomial optimization. It contains a compendium of the recent research activity that has taken place in these thrilling areas, and will appeal to doctoral" "students, young graduates, and experienced researchers alike.

The Handbook's thirty-one chapters are organized into four parts: "Theory," covering significant theoretical developments as well as the interactions between conic optimization and polynomial optimization;"Algorithms," documenting the directions of current algorithmic development;"Software," providing an overview of the state-of-the-art;"Applications," dealing with the application areas where semidefinite and conic optimization has made a significant impact in recent years.

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 unit commitment problem is a fundamental problem in the electric power industry. It addresses a fundamental decision that is taken when operating a power system, namely to set the schedule of power production for each generating unit in the system so that the demand for electricity is met at minimum cost. The schedule must also ensure that each unit operates within its technical limits; these typically include ramping constraints and minimum uptime/downtime constraints. Units that are scheduled to produce electricity during a given time period are said to be committed for that period. Unit Commitment in Electric Energy Systems presents the most relevant mathematical optimization models for the unit commitment problem. It is an ideal starting reference for practitioner and researchers interested in this important and challenging problem, as it introduces the key technical details and summarizing their significance.

Optimization is of critical importance in engineering. Engineers constantly strive for the best possible solutions, the most economical use of limited resources, and the greatest efficiency. As system complexity increases, these goals mandate the use of state-of-the-art optimization techniques. In recent years the theory and methodology of optimization have seen revolutionary improvements. Moreover, the exponential growth in computational power, along with the availability of multicore computing with virtually unlimited memory and storage capacity, has fundamentally changed what engineers can do to optimize their designs. This is a two-way process: engineers benefit from developments in optimization methodology, and challenging new classes of optimization problems arise from novel engineering applications. Advances and Trends in Optimization with Engineering Applications reviews 10 major areas of optimization and related engineering applications in a distinct part, providing a broad summary of state-of-the-art optimization techniques most important to engineering practice. Each part provides a clear overview of a specific area, followed by chapters detailing applications to a wide range of real-world problems. The book provides a solid foundation for engineers and mathematical optimizers alike who want to understand not only the importance of optimization methods to engineering but also the capabilities of current methods.