Effizienzsteigerung numerischer Verfahren der nichtlinearen Optimierung

Abstract

This thesis focuses on the development of multiple different techniques to improve the efficiency of nonlinear optimization algorithms. The contribution of this work can be divided in three main parts. Having a closer look on an Sequential Quadratic Programming (SQP) algorithm (namely the solver WORHP) theoretical results about the inertia of the system matrix in the case of SQP with interior-point-method for the solution of the subproblems are given and an adaptive relaxation scheme to handle inconsistent constraints is developed. Using parametric sensitivity analysis multiple algorithms to improve the SQP method are presented. These focus mainly on the handling of nonlinear constraints, but a new strategy to improve the necessary regularization of the Hessian of the Lagrangian is shown as well. In addition to these algorithmic advancements a technical discussion about parallelism for nonlinear programming is given and used to develop a new multi-core capable interface.