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Globally Convergent Second-order Schemes for Minimizing Twice-differentiable Functions

Author

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  • GRAPIGLIA, Geovani Nunes
  • NESTEROV, Yurii

Abstract

In this paper, we suggest new universal second-order methods for unconstrained minimization of twice-differentiable (convex or non-convex) objective function. For the current function, these methods automatically achieve the best possible global complexity estimates among different H older classes containing the Hessian of the objective. The universal methods for functional residual and for norm of the gradient are different. For development of the latter methods, we introduced a new line-search acceptance criterion, which can be seen as a nonlinear modification of the Armijo-Goldstein condition.

Suggested Citation

  • GRAPIGLIA, Geovani Nunes & NESTEROV, Yurii, 2016. "Globally Convergent Second-order Schemes for Minimizing Twice-differentiable Functions," LIDAM Discussion Papers CORE 2016028, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2016028
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2016.html
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    Cited by:

    1. C. P. Brás & J. M. Martínez & M. Raydan, 2020. "Large-scale unconstrained optimization using separable cubic modeling and matrix-free subspace minimization," Computational Optimization and Applications, Springer, vol. 75(1), pages 169-205, January.

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