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Robust Recursive Quadratic Programming Algorithm Model with Global and Superlinear Convergence Properties

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  • F. Facchinei

    (Università di Roma “La Sapienza,”)

Abstract

A new, robust recursive quadratic programming algorithm model based on a continuously differentiable merit function is introduced. The algorithm is globally and superlinearly convergent, uses automatic rules for choosing the penalty parameter, and can efficiently cope with the possible inconsistency of the quadratic search subproblem. The properties of the algorithm are studied under weak a priori assumptions; in particular, the superlinear convergence rate is established without requiring strict complementarity. The behavior of the algorithm is also investigated in the case where not all of the assumptions are met. The focus of the paper is on theoretical issues; nevertheless, the analysis carried out and the solutions proposed pave the way to new and more robust RQP codes than those presently available.

Suggested Citation

  • F. Facchinei, 1997. "Robust Recursive Quadratic Programming Algorithm Model with Global and Superlinear Convergence Properties," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 543-579, March.
    • Handle: RePEc:spr:joptap:v:92:y:1997:i:3:d:10.1023_a:1022655423083
    DOI: 10.1023/A:1022655423083
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    Citations

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    Cited by:

    1. Adam B. Levy, 2005. "Convergence of Successive Approximation Methods with Parameter Target Sets," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 765-784, August.
    2. Francisco Facchinei & Vyacheslav Kungurtsev & Lorenzo Lampariello & Gesualdo Scutari, 2021. "Ghost Penalties in Nonconvex Constrained Optimization: Diminishing Stepsizes and Iteration Complexity," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 595-627, May.
    3. Chen, M. J. & Huang, G. H., 2001. "A derivative algorithm for inexact quadratic program - application to environmental decision-making under uncertainty," European Journal of Operational Research, Elsevier, vol. 128(3), pages 570-586, February.
    4. J.L. Zhang & X.S. Zhang, 2003. "Sequential Penalty Algorithm for Nonlinear Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 118(3), pages 635-655, September.
    5. L. Qi & Y.F. Yang, 2002. "Globally and Superlinearly Convergent QP-Free Algorithm for Nonlinear Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 113(2), pages 297-323, May.

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