On the Convergence of Inexact Projection Primal First-Order Methods for Convex Minimization
Sign Up to like & getrecommendations! Published in 2018 at "IEEE Transactions on Automatic Control"
DOI: 10.1109/tac.2018.2805727
Abstract: It is well-known that primal first-order algorithms achieve sublinear (linear) convergence for smooth convex (smooth strongly convex) constrained minimization. However, these methods encounter numerical difficulties when the primal feasible set is complicated, since they require… read more here.
Keywords: first order; order methods; primal first; projection ... See more keywords
Restart of accelerated first order methods with linear convergence under a quadratic functional growth condition
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Transactions on Automatic Control"
DOI: 10.1109/tac.2022.3146054
Abstract: Accelerated first order methods, also called fast gradient methods, are popular optimization methods in the field of convex optimization. However, they are prone to suffer from oscillatory behaviour that slows their convergence when medium to… read more here.
Keywords: convergence; restart; order; order methods ... See more keywords
A Unification and Generalization of Exact Distributed First-Order Methods
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DOI: 10.1109/tsipn.2018.2846183
Abstract: Recently, there has been significant progress in the development of distributed first-order methods. In particular, Shi et al. (2015) on the one hand and Qu and Li (2017) and Nedic et al. (2016) on the other hand… read more here.
Keywords: unification generalization; order methods; distributed first; first order ... See more keywords
Optimal Fourth, Eighth and Sixteenth Order Methods by Using Divided Difference Techniques and Their Basins of Attraction and Its Application
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DOI: 10.3390/math7040322
Abstract: The principal objective of this work is to propose a fourth, eighth and sixteenth order scheme for solving a nonlinear equation. In terms of computational cost, per iteration, the fourth order method uses two evaluations… read more here.
Keywords: sixteenth order; eighth sixteenth; order; order methods ... See more keywords