subgradient projections

Seminorm-induced oblique projections for sparse nonlinear convex feasibility problems

  • Yair Censor
  • Alexander Segal
    • Categories Nonlinear Optimization, Nonlinear Systems and Least-Squares Tags , , ,

    Simultaneous subgradient projection algorithms for the convex feasibility problem use subgradient calculations and converge sometimes even in the inconsistent case. We devise an algorithm that uses seminorm-induced oblique projections onto super half-spaces of the convex sets, which is advantageous when the subgradient-Jacobian is a sparse matrix at many iteration points of the algorithm. Using generalized … Read more

    Projections Onto Super-Half-Spaces for Monotone Variational Inequality Problems in Finite-Dimensional Spaces

  • Yair Censor
  • Aviv Gibali
    • Categories Complementarity and Variational Inequalities Tags , ,

    The variational inequality problem (VIP) is considered here. We present a general algorithmic scheme which employs projections onto hyperplanes that separate balls from the feasible set of the VIP instead of projections onto the feasible set itself. Our algorithmic scheme includes the classical projection method and Fukushima’s subgradient projection method as special cases. Citation Technical … Read more

    On the behavior of subgradient projections methods for convex feasibility problems in Euclidean spaces

  • Dan Butnariu
  • Yair Censor
  • Ethan Hadar
  • Pini Gurfil
    • Categories Convex Optimization Tags , , ,

    We study some methods of subgradient projections for solving a convex feasibility problem with general (not necessarily hyperplanes or half-spaces) convex sets in the inconsistent case and propose a strategy that controls the relaxation parameters in a specific self-adapting manner. This strategy leaves enough user-flexibility but gives a mathematical guarantee for the algorithm’s behavior in … Read more