Stochastic and accelerated primal dual fixed point methods
Date:
Many important problems in data science and medical imaging—such as graphical lasso and computed tomography (CT) reconstruction—can be formulated as composite optimization problems. Although first-order primal-dual methods are widely adopted for their simplicity and low per-iteration cost, their performance often becomes unsatisfactory when applied to large-scale problems, which are increasingly common in practice. In this talk, we present three algorithmic extensions of the primal-dual fixed point (PDFP) method: the inertial PDFP (iPDFP), the stochastic PDFP (SPDFP), and the stochastic variance-reduced PDFP (SVRG-PDFP). These methods are specifically designed to address the computational challenges inherent in large-scale optimization tasks in data science and medical sciences. We provide convergence analyses for each algorithm and demonstrate their practical effectiveness through extensive numerical experiments.