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Complexity and global rates of trust-region methods based on probabilistic models

S. Gratton(serge.gratton***at***enseeiht.fr)
C. W. Royer(croyer2***at***wisc.edu)
L. N. Vicente(lnv***at***mat.uc.pt)
Z. Zhang(zaikun.zhang***at***polyu.edu.hk)

Abstract: Trust-region algorithms have been proved to globally converge with probability one when the accuracy of the trust-region models is imposed with a certain probability conditioning on the iteration history. In this paper, we study their complexity, providing global rates and worst case complexity bounds on the number of iterations (with overwhelmingly high probability), for both first and second order measures of optimality. Such results are essentially the same as the ones known for trust-region methods based on deterministic models. The derivation of the global rates and worst case complexity bounds follows closely from a study of direct-search methods based on the companion notion of probabilistic descent.

Keywords: Trust-region methods, probabilistic models, global rates, worst-case complexity

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Category 2: Stochastic Programming

Citation: S. Gratton, C. W. Royer, L. N. Vicente, and Z. Zhang, Complexity and global rates of trust-region methods based on probabilistic models, preprint 17-09, Dept. Mathematics, Univ. Coimbra.

Download: [PDF]

Entry Submitted: 02/17/2017
Entry Accepted: 02/17/2017
Entry Last Modified: 02/17/2017

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