Applied optimization and simulation form an area of engineering that sits between mathematics and computer science. They include computational tools used to solve important problems in engineering, economics, and all branches of science. Current concerns include the development and analysis of algorithms for the solution of problems of estimation, simulation and control of complex systems, and their implementations on computers. We are particularly interested in nonlinear optimization problems, which involve computationally intensive function evaluations. Such problems are ubiquitous; they arise in simulations with finite elements, in making statistical estimates, or simply in dealing with functions that are very difficult to handle. The comparability among the various techniques for numerical approximation through optimization algorithms is very important. What makes one formulation for the solution of a problem more desirable than another? This work requires the study and understanding of the delicate balance between the choices of mathematical approximation, computer architecture, data structures, and other factors-a balance crucial to the solution of many applications-driven problems.