Continuous nonlinear optimization for engineering applications in GAMS technology.

*(English)*Zbl 1395.90001
Springer Optimization and Its Applications 121. Cham: Springer (ISBN 978-3-319-58355-6/hbk; 978-3-319-58356-3/ebook). xxiv, 506 p. (2017).

This book contains a large collection of continuous nonlinear optimization applications from the real world. Its main purpose is to present the theoretical details and computational performances of algorithms used for solving those optimization problems using the high-level algebraic modeling language GAMS. General Algebraic Modeling System [A. Brooke et al., GAMS: a user’s guide. GAMS Development Corporation (1998)] is a high-level modeling system for expressing mathematical programming and optimization models using algebraic notation. It consists of a language compiler and a stable of integrated high-performance solvers. GAMS is tailored for complex, large scale modeling applications, and allows to build large maintainable models that can be adapted quickly to new situations.

Although GAMS is designed for modeling both linear, nonlinear and mixed integer optimization problems, this book focuses primarily on the local solutions of largescale, complex, continuous nonlinear optimization applications.

The book starts with an overview of constrained nonlinear optimization methods. Described are key aspects of mathematical modeling through modeling technologies based on algebraically oriented modeling languages. Next chapter introduces GAMS, being an algebraically oriented language that allows for a high-level algebraic representation of mathematical optimization models, and a compiler responsible for user interactions by compiling and executing user commands given in a GAMS source file, and a set of solvers to solve them. A group of 82 nonlinear optimization applications is given in the subsequent chapters. All these applications belong to the following domains of activity: linear algebra, nonlinear systems of equations, mechanical engineering, electrical engineering, chemical engineering, heat transfer and fluid dynamics, economic development, water management in river systems, robust stability analysis, and optimal control. For each application the mathematical model, together with its expression in GAMS and the corresponding solution given by the nonlinear optimization software CONOPT, KNITRO, MINOS, and SNOPT, is presented. Final chapter summarizes the conclusions of the book.

The audience: scientists and graduate students working with optimization methods to model and solve problems in mathematical programming, operations research, business, engineering, and industry. While only a basic programming background is required, understanding and utilizing GAMS technology capabilities to optimize algorithms for modeling and solving complex, large-scale, continuous nonlinear optimization problems or applications highly benefits from solid background in nonlinear optimization and linear algebra.

Although GAMS is designed for modeling both linear, nonlinear and mixed integer optimization problems, this book focuses primarily on the local solutions of largescale, complex, continuous nonlinear optimization applications.

The book starts with an overview of constrained nonlinear optimization methods. Described are key aspects of mathematical modeling through modeling technologies based on algebraically oriented modeling languages. Next chapter introduces GAMS, being an algebraically oriented language that allows for a high-level algebraic representation of mathematical optimization models, and a compiler responsible for user interactions by compiling and executing user commands given in a GAMS source file, and a set of solvers to solve them. A group of 82 nonlinear optimization applications is given in the subsequent chapters. All these applications belong to the following domains of activity: linear algebra, nonlinear systems of equations, mechanical engineering, electrical engineering, chemical engineering, heat transfer and fluid dynamics, economic development, water management in river systems, robust stability analysis, and optimal control. For each application the mathematical model, together with its expression in GAMS and the corresponding solution given by the nonlinear optimization software CONOPT, KNITRO, MINOS, and SNOPT, is presented. Final chapter summarizes the conclusions of the book.

The audience: scientists and graduate students working with optimization methods to model and solve problems in mathematical programming, operations research, business, engineering, and industry. While only a basic programming background is required, understanding and utilizing GAMS technology capabilities to optimize algorithms for modeling and solving complex, large-scale, continuous nonlinear optimization problems or applications highly benefits from solid background in nonlinear optimization and linear algebra.

Reviewer: Vladimír Lacko (Košice)

##### MSC:

90-02 | Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming |

90C30 | Nonlinear programming |

90-04 | Software, source code, etc. for problems pertaining to operations research and mathematical programming |

90C90 | Applications of mathematical programming |