Assessing the potential of interior methods for nonlinear optimization

Abstract. A series of numerical experiments with interior point (LOQO, KNITRO) and active-set sequential quadratic programming (SNOPT, filterSQP) codes are reported and analyzed. The tests were performed with small, medium-size and moderately large problems, and are examined by problem classes. Detailed observations on the performance of the codes, and several suggestions on how to improve them are presented. Overall, interior methods appear to be strong competitors of active-set SQP methods, but all codes show much room for improvement. 1 Introduction The goal of this paper is to evaluate the efficiency and robustness of interiormethods for nonlinear programming, and to assess their potential in the solution of very large problems. The hope is that this study will highlight someof the strengths and weaknesses of interior methods, suggest avenues for improving their performance, and identify classes of problems for which theyappear to be well suited. In order to conduct this evaluation we will perform numerical tests using two established interior point packages, LOQOand KNITRO, and will compare their performance with the state-of-the-art sequential quadratic programming codes, SNOPT and filterSQP. This willalso allow us to make some new observations about the numerical behavior of these two active-set SQP algorithms.The nonlinear programming problem will be written as minx f (x) (1a