Ernö Robert Csetnek

An inertial Tseng’s type proximal algorithm for nonsmooth and nonconvex optimization problems

  • Radu Ioan Bot
  • Ernö Robert Csetnek
    • Categories Nonsmooth Optimization Tags , , , , ,

    We investigate the convergence of a forward-backward-forward proximal-type algorithm with inertial and memory effects when minimizing the sum of a nonsmooth function with a smooth one in the absence of convexity. The convergence is obtained provided an appropriate regularization of the objective satisfies the Kurdyka-\L{}ojasiewicz inequality, which is for instance fulfilled for semi-algebraic functions. Article … Read more

    An inertial alternating direction method of multipliers

  • Radu Ioan Bot
  • Ernö Robert Csetnek
    • Categories Convex Optimization Tags , , , , , ,

    In the context of convex optimization problems in Hilbert spaces, we induce inertial effects into the classical ADMM numerical scheme and obtain in this way so-called inertial ADMM algorithms, the convergence properties of which we investigate into detail. To this aim we make use of the inertial version of the Douglas-Rachford splitting method for monotone … Read more

    Forward-Backward and Tseng’s Type Penalty Schemes for Monotone Inclusion Problems

  • Radu Ioan Bot
  • Ernö Robert Csetnek
    • Categories Convex Optimization Tags , , , , , , , ,

    We deal with monotone inclusion problems of the form $0\in Ax+Dx+N_C(x)$ in real Hilbert spaces, where $A$ is a maximally monotone operator, $D$ a cocoercive operator and $C$ the nonempty set of zeros of another cocoercive operator. We propose a forward-backward penalty algorithm for solving this problem which extends the one proposed by H. Attouch, … Read more

    On the convergence rate improvement of a primal-dual splitting algorithm for solving monotone inclusion problems

  • Radu Ioan Bot
  • Ernö Robert Csetnek
  • Andre Heinrich
    • Categories Convex Optimization Tags , , , , , , ,

    We present two modified versions of the primal-dual splitting algorithm relying on forward-backward splitting proposed in [21] for solving monotone inclusion problems. Under strong monotonicity assumptions for some of the operators involved we obtain for the sequences of iterates that approach the solution orders of convergence of ${\cal {O}}(\frac{1}{n})$ and ${\cal {O}}(\omega^n)$, for $\omega \in … Read more

    A primal-dual splitting algorithm for finding zeros of sums of maximally monotone operators

  • Radu Ioan Bot
  • Ernö Robert Csetnek
  • Andre Heinrich
    • Categories Convex Optimization Tags , , , , ,

    We consider the primal problem of finding the zeros of the sum of a maximally monotone operator with the composition of another maximally monotone operator with a linear continuous operator and a corresponding dual problem formulated by means of the inverse operators. A primal-dual splitting algorithm which simultaneously solves the two problems in finite-dimensional spaces … Read more