Object oriented implementation of a second-order optimization method

A structural optimization problem may be formulated as a single nonlinear program (NLP) and solved with a second-order method. This class of methods requires first and second derivatives of the objective function and of the inequality and equality constraints. When the size of the problem is large, derivative calculation may become tedious and error prone. Automatic differentiation (AD) techniques provide exact values for the derivatives without user intervention. In this paper the object oriented implementation of a Lagrange-Newton optimization algorithm is presented. An object oriented parser is used to interpret all the functions that describe the NLP. First and second derivatives are calculated with AD techniques using Rall numbers and their associated overloaded operators. A shape optimization example is presented to illustrate the proposed techniques.