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An inexact restoration strategy for the globalization of the sSQP method

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Abstract

A globally convergent algorithm based on the stabilized sequential quadratic programming (sSQP) method is presented in order to solve optimization problems with equality constraints and bounds. This formulation has attractive features in the sense that constraint qualifications are not needed at all. In contrast with classic globalization strategies for Newton-like methods, we do not make use of merit functions. Our scheme is based on performing corrections on the solutions of the subproblems by using an inexact restoration procedure. The presented method is well defined and any accumulation point of the generated primal sequence is either a Karush-Kuhn-Tucker point or a stationary (maybe feasible) point of the problem of minimizing the infeasibility. Also, under suitable hypotheses, the sequence generated by the algorithm converges Q-linearly. Numerical experiments are given to confirm theoretical results.

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Acknowledgements

The authors are thankful to the anonymous referees for the careful reading of the manuscript, helpful comments and suggestions.

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Authors and Affiliations

  1. Facultad de Matemática, Astronomía y Física, CIEM (CONICET), Universidad Nacional de Córdoba, Medina Allende s/n, Ciudad Universitaria, 5000, Córdoba, Argentina

    D. Fernández, E. A. Pilotta & G. A. Torres

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  1. D. Fernández
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  2. E. A. Pilotta
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  3. G. A. Torres
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Correspondence to E. A. Pilotta.

Additional information

This work was carried out with the aid of grants from ANPCyT, CONICET and SECyT-UNC.

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Fernández, D., Pilotta, E.A. & Torres, G.A. An inexact restoration strategy for the globalization of the sSQP method. Comput Optim Appl 54, 595–617 (2013). https://doi.org/10.1007/s10589-012-9502-y

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