The purpose of this book is to develop a wide collection of nonlinear optimization applications from the real-world expressed in the GAMS (General Algebraic Modeling System) language. The book is designed to present these applications in a very general form in such a way so that they could be very easily and quickly understood, updated, or modified to represent real situations from the real-world and is suitable for scientists working in various disciplines that use optimization methods to model and solve problems as well as mathematical programming researchers, operations research practitioners, and management consultants. This book is well suited as additional material for courses in optimization, operations research, decision making, and more. Modeling language in mathematical optimization supports symbols and nonlinear or differential expressions used in descriptions of optimization problems including the concepts of parameters, variables, constraints, and objective functions. Therefore, algebraic oriented modeling languages are the ones used in mathematical optimization systems.
Nonlinear Optimization Applications Using the GAMS Technology develops a wide spectrum of nonlinear optimization applications expressed in the GAMS (General Algebraic Modeling System) language. The book is highly self-contained and is designed to present applications in a general form that can be easily understood and quickly updated or modified to represent situations from the real world. The book emphasizes the local solutions of the large-scale, complex, continuous nonlinear optimization applications, and the abundant examples in GAMS are highlighted by those involving ODEs, PDEs, and optimal control. The collection of these examples will be useful for software developers and testers.
Chapter one presents aspects concerning the mathematical modeling process in the context of mathematical modeling technologies based on algebraic-oriented modeling languages. The GAMS technology is introduced in Chapter 2, mainly as a system for formulating and solving a large variety of general optimization models. The bulk of the 82 nonlinear optimization applications is given in Chapter 3.
This book is primarily intended to serve as a reference for graduate students and for scientists working in various disciplines of industry/mathematical programming that use optimization methods to model and solve problems. It is also well suited as supplementary material for seminars in optimization, operations research, and decision making, to name a few.
