REVIEW 2 cited by
First order optimization methods based on Hessian-driven Nesterov accelerated gradient flow
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
A novel dynamical inertial Newton system, which is called Hessian-driven Nesterov accelerated gradient (H-NAG) flow is proposed. Convergence of the continuous trajectory are established via tailored Lyapunov function, and new first-order accelerated optimization methods are proposed from ODE solvers. It is shown that (semi-)implicit schemes can always achieve linear rate and explicit schemes have the optimal(accelerated) rates for convex and strongly convex objectives. In particular, Nesterov's optimal method is recovered from an explicit scheme for our H-NAG flow. Furthermore, accelerated splitting algorithms for composite optimization problems are also developed.
Forward citations
Cited by 2 Pith papers
-
HNAG$^{++}$: An Accelerated Gradient Method with a Refined Asymptotic Rate for Strongly Convex Optimization
A Lyapunov/ODE-based analysis yields HNAG+ (rate 1-2/√κ) and HNAG++ (asymptotic rate 1-2√(2/κ) under Hölder Hessians).
-
Continuous and discrete-time accelerated methods for an inequality constrained convex optimization problem
A Bregman Lagrangian with a logarithmic barrier leads to a continuous-time dynamical system and discrete accelerated methods that converge to the solution of convex inequality-constrained problems.
Discussion (0). Continue with ORCID to comment.