Nonlinear Stepsize Control Algorithms: Complexity Bounds for First- and Second-Order Optimality
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- 作者：Geovani Nunes Grapiglia ; Jinyun Yuan…
- 关键词：Worst ; case complexity ; Trust ; region methods ; Regularization methods ; Unconstrained optimization
- 刊名：Journal of Optimization Theory and Applications
- 出版年：2016
- 出版时间：December 2016
- 年：2016
- 卷：171
- 期：3
- 页码：980-997
- 全文大小：
- 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operation Research/Decision Theory;
- 出版者：Springer US
- ISSN：1573-2878
- 卷排序：171
文摘
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.