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Hybrid globalization of convergence of subspace-stabilized sequential quadratic programming method
Vestnik rossijskih universitetov. Matematika, Tome 24 (2019) no. 126, pp. 150-165 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: sequential quadratic programming, degenerate solutions, noncritical Lagrange multiplier, dual stabilization, globalization of convergence. 
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N. G. Zhurbenko; A. F. Izmailov; E. I. Uskov. Hybrid globalization of convergence of subspace-stabilized sequential quadratic programming method. Vestnik rossijskih universitetov. Matematika, Tome 24 (2019) no. 126, pp. 150-165. http://geodesic.mathdoc.fr/item/VTAMU_2019_24_126_a1/

[1] A. F. Izmailov, M. V. Solodov, Newton-Type Methods for Optimization and Variational Problems, Springer Series in Operations Research and Financial Engineering, Springer, Cham, 2014 | DOI | MR

[2] A. F. Izmailov, M. V. Solodov, Numerical Methods of Optimization, Second ed., Fizmatlit, Moscow, 2008 (In Russian) | MR

[3] S. J. Wright, “Superlinear convergence of a stabilized SQP method to a degenerate solution”, Comput. Optim. Appl., 11 (1998), 253–275 | DOI | MR | Zbl

[4] A. F. Izmailov, M. V. Solodov, “Stabilized SQP revisited”, Math. Program., 133 (2012), 93–120 | DOI | MR | Zbl

[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)

[6] P. E. Gill, D. P. Robinson, “A primal-dual augmented Lagrangian”, Comput. Optim. Appl., 51 (2012), 1–25 | DOI | MR | Zbl

[7] P. E. Gill, D. P. Robinson, “A globally convergent stabilized SQP method”, SIAM J. Optim. Appl., 23 (2013), 1983–2010 | DOI | MR | Zbl

[8] D. Fernandez, E. A. Pilotta, G. A. Torres, “An inexact restoration strategy for the globalization of the sSQP method”, Comput. Optim. Appl., 54 (2013), 595–617 | DOI | MR | Zbl

[9] A. F. Izmailov, M. V. Solodov, E. I. Uskov, “Combining stabilized SQP with the augmented Lagrangian algorithm”, Comput. Optim. Appl., 62 (2015), 33–73 | DOI | MR

[10] A. F. Izmailov, M. V. Solodov, E. I. Uskov, “Globalizing stabilized sequential quadratic programming method by smooth primal-dual exact penalty function”, J. Optim. Theory. Appl., 69 (2016), 148–178 | DOI | MR

[11] P. E. Gill, V. Kungurtsev, D. P. Robinson, “A stabilized SQP method: global convergence”, IMA Journal of Numerical Analysis, 37 (2017), 407–443 | DOI | MR | Zbl

[12] P. E. Gill, V. Kungurtsev, D. P. Robinson, “A stabilized SQP method: superlinear convergence”, Math. Program., 163 (2017), 369–410 | DOI | MR | Zbl

[13] A. F. Izmailov, E. I. Uskov, “Subspace-stabilized sequential quadratic programming”, Comput. Optim. Appl., 67 (2017), 129–154 | DOI | MR | Zbl

[14] E. M. E. Mostafa, L. N. Vicente, S. J. Wright, “Numerical behavior of a stabilized SQP method for degenerate NLP problems”, Global Optimization and Constraint Satisfaction., Lecture Notes in Computer Science 2861., Springer, Berlin, 2003, 123–141 | DOI | Zbl

[15] A. F. Izmailov, M. V. Solodov, “Newton-type methods for optimization problems without constraint qualifications”, SIAM J. Optim., 15 (2004), 210–228 | DOI | MR | Zbl

[16] J. Nocedal, S. J. Wright, Numerical Optimization, Second ed., Springer, New York, 2006 | MR | Zbl

[17] A. F. Izmailov, M. V. Solodov, “On attraction of Newton-type iterates to multipliers violating second-order sufficiency conditions”, Math. Program., 117 (2009), 271–304 | DOI | MR | Zbl

[18] E. D. Dolan, J. J. More, “Benchmarking optimization software with performance profiles”, Math. Program., 91 (2002), 201–213 | DOI | MR | Zbl