New over-relaxed monotone fast iterative shrinkage-thresholding algorithm for linear inverse problems

The over-relaxed monotone fast iterative shrinkage-thresholding algorithm (OMFISTA) needs to satisfy a complex convergence condition with respect to its additional parameters. To simplify the convergence condition, this study proposes a new OMFISTA, termed OMFISTAv2, using a parameter setting strategy which will derive a simple sufficient condition with respect to the additional parameters to guarantee the convergence of OMFISTAv2. Moreover, the authors find experimentally that OMFISTAv2 can accelerate MFISTA in some cases where the system matrix is ill-conditioned or rank-deficient, while OMFISTA cannot.