Rafiq Mansour

The alternating simultaneous Halpern-Lions-Wittmann-Bauschke algorithm for finding the best approximation pair for two disjoint intersections of convex sets

  • Yair Censor
  • Rafiq Mansour
  • Daniel Reem
    • Categories Approximation Algorithms, Constrained Nonlinear Optimization, Convex Optimization Tags , , , , ,

    Given two nonempty and disjoint intersections of closed and convex subsets, we look for a best approximation pair relative to them, i.e., a pair of points, one in each intersection, attaining the minimum distance between the disjoint intersections. We propose an iterative process based on projections onto the subsets which generate the intersections. The process … Read more

    Convergence Analysis of Processes with Valiant Projection Operators in Hilbert Space

  • Yair Censor
  • Rafiq Mansour
    • Categories Constrained Nonlinear Optimization, Convex Optimization

    Convex feasibility problems require to find a point in the intersection of a finite family of convex sets. We propose to solve such problems by performing set-enlargements and applying a new kind of projection operators called valiant projectors. A valiant projector onto a convex set implements a special relaxation strategy, proposed by Goffin in 1971, … Read more

    New Douglas-Rachford algorithmic structures and their convergence analyses

  • Yair Censor
  • Rafiq Mansour
    • Categories Convex Optimization Tags , ,

    In this paper we study new algorithmic structures with Douglas- Rachford (DR) operators to solve convex feasibility problems. We propose to embed the basic two-set-DR algorithmic operator into the String-Averaging Projections (SAP) and into the Block-Iterative Pro- jection (BIP) algorithmic structures, thereby creating new DR algo- rithmic schemes that include the recently proposed cyclic Douglas- … Read more