1 Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Center for Bachelor of Engineering Studies, Technical University of Denmark3 Department of Applied Mathematics and Computer Science, Technical University of Denmark4 Department of Electrical Engineering, Technical University of Denmark
A theoretical treatment of singularities in nonlinear minimax optimization problems, which allows for a classification in regular and singular problems, is presented. A theorem for determining a singularity that is present in a given problem is formulated. A group of problems often used in the literature to test nonlinear minimax algorithms, i.e., minimax design of multisection quarter-wave transformers, is shown to exhibit singularities and the reason for this is pointed out. Based on the theoretical results presented an algorithm for nonlinear minimax optimization is developed. The new algorithm maintains the quadratic convergence property of a recent algorithm by Madsen et al. when applied to regular problems and it is demonstrated to significantly improve the final convergence on singular problems.
Ieee Transactions on Circuits and Systems, 1976, Vol 23, Issue 7, p. 456-460