$R$-linear convergence rate

Fixed point continuation algorithm with extrapolation for Schatten p-quasi-norm regularized matrix optimization problems

  • Peng Dingtao
    • Categories Nonsmooth Optimization, Unconstrained Optimization Tags , , , ,

    In this paper, we consider a general low-rank matrix optimization problem which is modeled by a general Schatten p-quasi-norm (${\rm 0<p<1}$) regularized matrix optimization. For this nonconvex nonsmooth and non-Lipschitz matrix optimization problem, based on the matrix p-thresholding operator, we first propose a fixed point continuation algorithm with extrapolation (FPCAe) for solving it. Secondly, we … Read more

    Solution to a Monotone Inclusion Problem using the Relaxed Peaceman-Rachford Splitting Method: Convergence and its Rates

  • Chee-Khian Sim
    • Categories Convex and Nonsmooth Optimization Tags , , , ,

    We consider the convergence behavior using the relaxed Peaceman-Rachford splitting method to solve the monotone inclusion problem $0 \in (A + B)(u)$, where $A, B: \Re^n \rightrightarrows \Re^n$ are maximal $\beta$-strongly monotone operators, $n \geq 1$ and $\beta > 0$. Under a technical assumption, convergence of iterates using the method on the problem is proved … Read more