On Inexact Accelerated Proximal Gradient Methods with Relative Error Rules

Understand

One of the most popular and important first-order iterations that provides optimal complexity of the classical proximal gradient method (PGM) is the "Fast Iterative Shrinkage/Thresholding Algorithm" (FISTA).

• In this paper, two inexact versions of FISTA for minimizing the sum of two convex functions are studied.
• The proposed schemes inexactly solve their subproblems by using relative error criteria instead of exogenous and diminishing error rules.
• When the evaluation of the proximal operator is difficult, inexact versions of FISTA are necessary and the relative error rules proposed here may have certain advantages over previous error rules.