Affiliation:
1. V. M. Glushkov Institute of Cybernetics of NAS of Ukraine
2. Lomonosov Moscow State University
3. Derzhavin Tambov State University
Abstract
Local superlinear convergence of the stabilized sequential quadratic programming method is established under very weak assumptions not involving any constraint qualification conditions. However, all attempts to globalize convergence of this method inevitably face principal difficulties related to the behavior of this method when the iterates are still relatively far from solutions. Specifically, the stabilized sequential quadratic programming method has a tendency to generate long sequences of short steps before its superlinear convergence shows up. To that end, the so-called subspace-stabilized sequential quadratic programming method has been proposed, demonstrating better “semi-local” behavior, and hence, more suitable for development of practical algorithms on its basis. In this work we propose two techniques for hybrid globalization of convergence of this method: algorithm with backups, and algorithm with records.We provide theoretical results on convergence and rate of convergence of these algorithms, as well as some results of their numerical testing.
Publisher
Tambov State University - G.R. Derzhavin
Reference18 articles.
1. A. F. Izmailov, M. V. Solodov, Newton-Type Methods for Optimization and Variational Problems, Springer Series in Operations Research and Financial Engineering, Cham: Springer, 2014.
2. A. F. Izmailov, M. V. Solodov, Numerical Methods of Optimization, Second ed., Fizmatlit, Moscow, 2008 (In Russian).
3. S. J. Wright, “Superlinear convergence of a stabilized SQP method to a degenerate solution”, Comput. Optim. Appl., 11 (1998), 253–275.
4. A. F. Izmailov, M. V. Solodov, “Stabilized SQP revisited”, Math. Program., 133 (2012), 93–120.
5. A. F. Izmailov, A. M. Krylova, E. I. Uskov, “Hybrid globalization of stabilized sequential quadratic programming method”, Theoretical and applied problems of nonlinear analysis, Computing Center RAS, Moscow, 2011, 47–66 (In Russian).