Limited Memory BFGS method for Sparse and Large-Scale Nonlinear Optimization

Optimization-based control systems are used in many areas of application, including aerospace engineering, economics, robotics and automotive engineering. This work was motivated by the demand for a large-scale sparse solver for this problem class. The sparsity property of the problem is used for the computational efficiency regarding performance and memory consumption. This includes an efficient storing of the occurring matrices and vectors and an appropriate approximation of the Hessian matrix, which is the main subject of this work. Thus, a so-called the limited memory BFGS method has been developed. The limited memory BFGS method, has been implemented in a software library for solving the nonlinear optimization problems, WORHP. Its solving performance has been tested on different optimal control problems and test sets.