A Line-Search Algorithm Inspired by the Adaptive Cubic Regularization Framework and Complexity Analysis

Bergou, El Houcine, Diouane, Youssef and Gratton, Serge (2018) A Line-Search Algorithm Inspired by the Adaptive Cubic Regularization Framework and Complexity Analysis. Journal of Optimization Theory and Applications, vol. 178 (n° 3). pp. 885-913.

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Abstract

Adaptive regularized framework using cubics has emerged as an alternative to line-search and trust-region algorithms for smooth nonconvex optimization, with an optimal complexity amongst second-order methods. In this paper, we propose and analyze the use of an iteration dependent scaled norm in the adaptive regularized framework using cubics. Within such scaled norm, the obtained method behaves as a line-search algorithm along the quasi- Newton direction with a special backtracking strategy. Under appropriate assumptions, the new algorithm enjoys the same convergence and complexity properties as adaptive regularized algorithm using cubics. The complexity for finding an approximate first-order stationary point can be improved to be optimal whenever a second order version of the proposed algorithm is regarded. In a similar way, using the same scaled norm to define the trust-region neighborhood, we show that the trust-region algorithm behaves as a line-search algorithm. The good potential of the obtained algorithms is shown on a set of large scale optimization problems.

Item Type: Article
Language: English
Date: 2018
Refereed: Yes
Uncontrolled Keywords: Nonlinear optimization - Unconstrained optimization - Line-search methods - Adaptive regularized framework using cubics - Trust-region methods - Worst-case complexity
Subjects: H- INFORMATIQUE
Divisions: Institut de Recherche en Informatique de Toulouse
Site: UT1
Date Deposited: 22 Jan 2019 15:06
Last Modified: 21 Mar 2019 15:35
URI: http://publications.ut-capitole.fr/id/eprint/30784

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