Submitted

Accelerated Transformed Primal Dual Methods for Affine Equality Constrained Optimization Problems

Long Chen, and Jingrong Wei

Submitted

arXiv   Bibtex

ABSTRACT:

Accelerated transformed primal--dual (ATPD) methods are
proposed for smooth convex optimization problems with affine equality
constraints. In the strongly convex regime, ATPD achieves an
accelerated linear convergence rate, while in the convex regime, it
attains an accelerated sublinear rate. The acceleration mechanism is
unified through an exponentially stable ATPD flow at the continuous
level, whose discretization yields practical algorithms. The resulting
methods match the known lower bounds on first-order oracle complexity
in terms of gradient evaluations and matrix--vector
products. Numerical experiments confirm the theoretical results and
demonstrate the efficiency of the proposed methods.