Applications of Continuous Nonlinear Optimization

Abstract

A number of 18 real continuous nonlinear optimization applications are presented in this chapter. These are used for numerical experiments and comparisons among the algorithms described in this book. For each application, the mathematical model, its GAMS representation, and the solution are given. GAMS is a standard technology for modeling and solving large-scale linear and nonlinear optimization applications. It is characterized by a very powerful language and a large number of different advanced optimization algorithms which are imbedded in this technology. The syntax of the GAMS language is not too complicated and practically all types of difficult nonlinear optimization applications can be represented and solved. Additionally, the nonlinear optimal control application, by discretization, can also be represented and solved by GAMS. Therefore, in this chapter, we include both continuous nonlinear optimization applications and some optimal control problems from different areas of activity. Some applications are from mechanical, electrical, and chemical engineering, heat transfer and fluid dynamics, and economic development. Others are from optimal control. The purpose is to present these applications in algebraic form and to see how all these can be represented and solved in GAMS. The solutions of these applications are determined by the optimization algorithms imbedded in the GAMS technology (MINOS, CONOPT, KNITRO, SNOPT, IPOPT) as well as some other packages described in this book (SPENBAR, DONLP, NLPQLP, filterSD) not imbedded in GAMS.