A control-theoretic perspective on optimal high-order optimization

We provide a control-theoretic perspective on optimal tensor algorithms for minimizing a convex function in a finite-dimensional Euclidean space. Given a function Φ : R d → R that is convex and twice continuously differentiable, we study a closed-loop control system that is governed by the operators...

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Bibliographic Details
Published in:	Mathematical programming Vol. 195; no. 1-2; pp. 929 - 975
Main Authors:	Lin, Tianyi, Jordan, Michael I.
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2022 Springer Springer Nature B.V
Subjects:	Algorithms Calculus of Variations and Optimal Control; Optimization Combinatorics Continuous time systems Control systems Control theory Convergence Euclidean geometry Euclidean space Feedback control Fixed points (mathematics) Full Length Paper Inventory control Laws, regulations and rules Liapunov functions Mathematical analysis Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Operators (mathematics) Optimization Tensors Theoretical Uniqueness Iteration complexity 68Q25 Convex optimization 90C25 High-order tensor algorithm Optimal acceleration Feedback control 49M37 Closed-loop control system 90C60 37N40
ISSN:	0025-5610, 1436-4646
Online Access:	Get full text
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