ABSTRACT
This chapter introduces nonlinear optimization with emphasis on the selected algorithms. Nonlinear optimization methods can be generally classified into unconstrained optimization methods and constrained optimization methods. Structural design problems are commonly formulated for constrained optimization which, however, can be solved by employing unconstrained optimization algorithms in the constrained optimization formulation. An approach to the optimization of a nonlinear problem is to replace it with a sequence of linear programming problems. The numerical method for this approach is to compute design change by using Taylor's expansion for the cost and constraint functions. Both interior and exterior function methods are commonly classified as transformation methods. Since the transformation method is to solve a constrained optimization problem by using a non-constrained optimization technique, the basic idea is to construct a composite function using an objective function and a constraint function with certain parameters.
