Optimization and Its Applications with GAMS

Textbook:Nonlinear Optimization Applications Using the GAMS Technology
Author(s): Neculai Andrei

Description:
Chapter 1 presents some aspects concerning the mathematical modeling process in the context of mathematical modeling technologies based on algebraically oriented modeling languages. It is emphasized that a mathematical model has three forms of representation: an algebraic-differential one using mathematical symbols, an external one using an algebraically oriented mathematical modeling language (e.g., GAMS, AMPL, ALLO), and an internal representation that is mainly an informatics description including different files and databases directly admitted by any optimizer. Chapter 2 introduces the GAMS technology. GAMS is mainly a system for formulating and solving a wide variety of general optimization models. It consists of an algebraically oriented language that allows for a high-level algebraic representation of mathematical optimization models, a compiler that is 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 Chaps. 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12. 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. Chapter 13 summarizes the conclusions of the coursebook.