Average Curvature FISTA for Nonconvex Smooth Composite Optimization Problems

A previous authors’ paper introduces an accelerated composite gradient (ACG) variant, namely AC-ACG, for solving nonconvex smooth composite optimization (N-SCO) problems. In contrast to other ACG variants, AC-ACG estimates the local upper curvature of the N-SCO problem by using the average of the observed upper-Lipschitz curvatures obtained during the previous iterations, and uses this estimation … Read more

Some Modified Fast Iteration Shrinkage Thresholding Algorithms with a New Adaptive Non-monotone Stepsize Strategy for Nonsmooth and Convex Minimization Problems

The ” fast iterative shrinkage-thresholding algorithm ” (FISTA) is one of the most famous first order optimization scheme, and the stepsize, which plays an important role in theoretical analysis and numerical experiment, is always determined by a constant related to the Lipschitz constant or by a backtracking strategy. In this paper, we design a new … Read more

On Inexact Accelerated Proximal Gradient Methods with Relative Error Rules

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 … Read more

Adaptive Fista

In this paper we propose an adaptively extrapolated proximal gradient method, which is based on the accelerated proximal gradient method (also known as FISTA), however we locally optimize the extrapolation parameter by carrying out an exact (or inexact) line search. It turns out that in some situations, the proposed algorithm is equivalent to a class … Read more

Convergence Analysis of ISTA and FISTA for “Strongly + Semi” Convex Programming

The iterative shrinkage/thresholding algorithm (ISTA) and its faster version FISTA have been widely used in the literature. In this paper, we consider general versions of the ISTA and FISTA in the more general “strongly + semi” convex setting, i.e., minimizing the sum of a strongly convex function and a semiconvex function; and conduct convergence analysis … Read more