On the Performance of NLP Solvers Within Global MINLP Solvers
Solving mixed-integer nonlinear programs (MINLPs) to global optimality efficiently requires fast solvers for continuous sub-problems. These appear in, e.g., primal heuristics, convex relaxations, and bound tightening methods. Two of the best performing algorithms for these sub-problems are Sequential Quadratic Programming (SQP) and Interior Point Methods. In this paper we study the impact of different SQP and Interior Point implementations on important MINLP solver components that solve a sequence of similar NLPs. We use the constraint integer programming framework SCIP for our computational studies.
KeywordsMixed-integer nonlinear programming Interior point Sequential quadratic programming Global optimization
This work has been supported by the Research Campus MODAL Mathematical Optimization and Data Analysis Laboratories funded by the Federal Ministry of Education and Research (BMBF Grant 05M14ZAM).
- 1.Grossmann, I. E., & Sahinidis, N. V. (2002). Special issue on mixed integer programming and its application to engineering, part I. Optimization and engineering, 3(4).Google Scholar
- 5.Berthold, T. (2014). Heuristic algorithms in global MINLP solvers. Ph.D. thesis, Technische Universität BerlinGoogle Scholar
- 9.Vigerske, S., & Gleixner, A. SCIP: Global optimization of mixed-integer nonlinear programs in a branch-and-cut framework. Optimization Methods and Software (to appear)Google Scholar
- 12.Fletcher, R., & Leyffer, S. (1998). User manual for filterSQP. Numerical analysis report NA/181, Department of Mathematics, University of Dundee, Scotland.Google Scholar
- 13.Kuhlmann, R., & Büskens, C. (2017). A primal-dual augmented Lagrangian penalty-interior-point filter line search algorithm. Technical report, Universität Bremen.Google Scholar