Tensor Methods for Minimizing Convex Functions with Hölder Continuous Higher-Order Derivatives

DOI10.1137/19M1259432zbMath1451.90119arXiv1904.12559OpenAlexW3164331286MaRDI QIDQ4971023

Geovani Nunes Grapiglia, Yu. E. Nesterov

Publication date: 8 October 2020

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.12559

zbMATH Keywords

unconstrained minimizationhigh-order methodsHölder conditiontensor methodsworst-case global complexity bounds

Mathematics Subject Classification ID

Convex programming (90C25) Nonlinear programming (90C30) Convexity of real functions of several variables, generalizations (26B25)

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Tensor methods for finding approximate stationary points of convex functions, Inexact basic tensor methods for some classes of convex optimization problems, Local convergence of tensor methods, Accelerated meta-algorithm for convex optimization problems, Super-Universal Regularized Newton Method, Efficiency of higher-order algorithms for minimizing composite functions, Adaptive Third-Order Methods for Composite Convex Optimization, Near-Optimal Hyperfast Second-Order Method for Convex Optimization, An adaptive high order method for finding third-order critical points of nonconvex optimization, Unified Acceleration of High-Order Algorithms under General Hölder Continuity, A control-theoretic perspective on optimal high-order optimization, On complexity and convergence of high-order coordinate descent algorithms for smooth nonconvex box-constrained minimization, On inexact solution of auxiliary problems in tensor methods for convex optimization, High-Order Optimization Methods for Fully Composite Problems

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