Submitted

Accelerated Mirror Descent Method through Variable and Operator Splitting

Long Chen, Hao Luo, Jingrong Wei, Zeyi Xu, Yuan Yao

Submitted

arXiv   Bibtex

ABSTRACT:

Mirror descent uses the mirror function to encode geometry
and constraints, improving convergence while preserving
feasibility. Accelerated Mirror Descent Methods (Acc-MD) are derived
from a discretization of an accelerated mirror ODE system using a
variable--operator splitting framework. A geometric assumption, termed
the Generalized Cauchy-Schwarz (GCS) condition, is introduced to
quantify the compatibility between the objective and the mirror
geometry, under which the first accelerated linear convergence for
Acc-MD on a broad class of problems is established. Numerical
experiments on smooth and composite optimization tasks demonstrate
that Acc-MD consistently outperforms existing accelerated variants,
both theoretically and empirically.