block-iterative algorithms

Block-Iterative Algorithms with Underrelaxed Bregman Projections

  • Yair Censor
  • Gabor T. Herman
    • Categories Constrained Nonlinear Optimization, Convex Optimization Tags , , , ,

    The notion of relaxation is well understood for orthogonal projections onto convex sets. For general Bregman projections it was considered only for hyperplanes and the question of how to relax Bregman projections onto convex sets that are not linear (i.e., not hyperplanes or half-spaces) has remained open. A definition of underrelaxation of Bregman projections onto … Read more

    Block-iterative algorithms with diagonally scaled oblique projections for the linear feasibility problem

  • Yair Censor
  • Tommy Elfving
    • Categories Convex Optimization, Linear Programming Tags , , , , ,

    We formulate a block-iterative algorithmic scheme for the solution of systems of linear inequalities and/or equations and analyze its convergence. This study provides as special cases proofs of convergence of (i) the recently proposed Component Averaging (CAV) method of Censor, Gordon and Gordon ({\it Parallel Computing}, 27:777–808, 2001), (ii) the recently proposed Block-Iterative CAV (BICAV) … Read more