Nonlinear Stepsize Control Algorithms: Complexity Bounds for First- and Second-Order Optimality

Geovani Nunes Grapiglia (), Jinyun Yuan () and Ya-xiang Yuan ()
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Geovani Nunes Grapiglia: Universidade Federal do Paraná, Centro Politécnico
Jinyun Yuan: Universidade Federal do Paraná, Centro Politécnico
Ya-xiang Yuan: Academy of Mathematics and Systems Science, Chinese Academy of Sciences

Journal of Optimization Theory and Applications, 2016, vol. 171, issue 3, No 12, 980-997

Abstract: Abstract A nonlinear stepsize control (NSC) framework has been proposed by Toint (Optim Methods Softw 28:82–95, 2013) for unconstrained optimization, generalizing several trust-region and regularization algorithms. More recently, worst-case complexity bounds to achieve approximate first-order optimality were proved by Grapiglia, Yuan and Yuan (Math Program 152:491–520, 2015) for the generic NSC framework. In this paper, improved complexity bounds for first-order optimality are obtained. Furthermore, complexity bounds for second-order optimality are also provided.

Keywords: Worst-case complexity; Trust-region methods; Regularization methods; Unconstrained optimization; 90C30; 65K05; 49M37; 49M15; 90C29; 90C60; 68Q25 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-016-1007-x

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