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

Gratton, Serge and Royer, Clément and Vicente, Luis and Zhang, Zaikun Complexity and global rates of trust-region methods based on probabilistic mode. (2018) IMA Journal of Numerical Analysis, 38 (3). 1579-1597. ISSN 0272-4979

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Official URL: https://doi.org/10.1093/imanum/drx043

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.

Item Type:Article
Additional Information:http://www.optimization-online.org/DB_HTML/2017/02/5866.html
HAL Id:hal-02147973
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > Universidade de Coimbra (PORTUGAL)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Hong Kong Polytechnic University - PolyU (CHINA)
Other partners > University of Wisconsin - Madison (USA)
Laboratory name:
Funders:
Hong Kong Polytechnic University (CHINA)
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Deposited By: IRIT IRIT
Deposited On:14 May 2019 08:48

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