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

Nunes Grapiglia, Geovani;Yuan, Jinyun;Yuan, Ya-xiang
(2016) Journal of Optimization Theory and Applications — Vol. 171, n° 3, p. 980-997 (2016)

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Abstract
(en) 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.
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  • Universidade Federal do ParanáDepartamento de Matemática

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Nunes Grapiglia, G., Yuan, J., & Yuan, Y.-x. (2016). Nonlinear Stepsize Control Algorithms: Complexity Bounds for First- and Second-Order Optimality. Journal of Optimization Theory and Applications, 171(3), 980-997. https://doi.org/10.1007/s10957-016-1007-x (Original work published 2016)