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Accelerating convergence of a globalized sequential quadratic programming method to critical Lagrange multipliers

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  • A. F. Izmailov

    (Lomonosov Moscow State University (MSU))

Abstract

This paper concerns the issue of asymptotic acceptance of the true Hessian and the full step by the sequential quadratic programming algorithm for equality-constrained optimization problems. In order to enforce global convergence, the algorithm is equipped with a standard Armijo linesearch procedure for a nonsmooth exact penalty function. The specificity of considerations here is that the standard assumptions for local superlinear convergence of the method may be violated. The analysis focuses on the case when there exist critical Lagrange multipliers, and does not require regularity assumptions on the constraints or satisfaction of second-order sufficient optimality conditions. The results provide a basis for application of known acceleration techniques, such as extrapolation, and allow the formulation of algorithms that can outperform the standard SQP with BFGS approximations of the Hessian on problems with degenerate constraints. This claim is confirmed by some numerical experiments.

Suggested Citation

  • A. F. Izmailov, 2021. "Accelerating convergence of a globalized sequential quadratic programming method to critical Lagrange multipliers," Computational Optimization and Applications, Springer, vol. 80(3), pages 943-978, December.
    • Handle: RePEc:spr:coopap:v:80:y:2021:i:3:d:10.1007_s10589-021-00317-z
    DOI: 10.1007/s10589-021-00317-z
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    References listed on IDEAS

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    1. A. Izmailov & M. Solodov & E. Uskov, 2015. "Combining stabilized SQP with the augmented Lagrangian algorithm," Computational Optimization and Applications, Springer, vol. 62(2), pages 405-429, November.
    2. A. Izmailov & M. Solodov, 2015. "Rejoinder on: Critical Lagrange multipliers: what we currently know about them, how they spoil our lives, and what we can do about it," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 48-52, April.
    3. A. Izmailov & M. Solodov, 2015. "Critical Lagrange multipliers: what we currently know about them, how they spoil our lives, and what we can do about it," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 1-26, April.
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