Simeon Reich

The Split Common Null Point Problem

  • Charles Byrne
  • Yair Censor
  • Aviv Gibali
  • Simeon Reich
    • Categories Complementarity and Variational Inequalities, Convex Optimization

    We introduce and study the Split Common Null Point Problem (SCNPP) for set-valued maximal monotone mappings in Hilbert spaces. This problem generalizes our Split Variational Inequality Problem (SVIP) [Y. Censor, A. Gibali and S. Reich, Algorithms for the split variational inequality problem, Numerical Algorithms 59 (2012), 301–323]. The SCNPP with only two set-valued mappings entails … Read more

    A von Neumann Alternating Method for Finding Common Solutions to Variational Inequalities

  • Yair Censor
  • Aviv Gibali
  • Simeon Reich
    • Categories Complementarity and Variational Inequalities, Nonlinear Optimization Tags , , , , , , , ,

    Modifying von Neumann’s alternating projections algorithm, we obtain an alternating method for solving the recently introduced Common Solutions to Variational Inequalities Problem (CSVIP). For simplicity, we mainly confine our attention to the two-set CSVIP, which entails finding common solutions to two unrelated variational inequalities in Hilbert space. Citation Nonlinear Analysis Series A: Theory, Methods & … Read more

    Weak and Strong Convergence of Algorithms for the Split Common Null Point Problem

  • Charles Byrne
  • Yair Censor
  • Aviv Gibali
  • Simeon Reich
    • Categories Complementarity and Variational Inequalities, Convex Optimization, Nonlinear Optimization

    We introduce and study the Split Common Null Point Problem (SCNPP) for set-valued maximal monotone mappings in Hilbert space. This problem generalizes our Split Variational Inequality Problem (SVIP) [Y. Censor, A. Gibali and S. Reich, Algorithms for the split variational inequality problem, Numerical Algorithms, accepted for publication, DOI 10.1007/s11075-011-9490-5]. The SCNPP with only two set-valued … Read more

    The Split Variational Inequality Problem

  • Yair Censor
  • Aviv Gibali
  • Simeon Reich
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags , , , ,

    We propose a new variational problem which we call the Split Variational Inequality Problem (SVIP). It entails finding a solution of one Variational Inequality Problem (VIP), the image of which under a given bounded linear transformation is a solution of another VIP. We construct iterative algorithms that solve such problems, under reasonable conditions, in Hilbert … Read more

    General algorithmic frameworks for online problems

  • Yair Censor
  • Simeon Reich
  • Alexander J. Zaslavski
    • Categories Basic Sciences Applications, Convex Optimization Tags , , , , ,

    We study general algorithmic frameworks for online learning tasks. These include binary classification, regression, multiclass problems and cost-sensitive multiclass classification. The theorems that we present give loss bounds on the behavior of our algorithms that depend on general conditions on the iterative step sizes. Citation International Journal of Pure and Applied Mathematics, Vol. 46 (2008), … Read more

    Finding the projection of a point onto the intersection of convex sets via projections onto halfspaces

  • L.M. Bregman
  • Yair Censor
  • Simeon Reich
  • Y. Zepkowitz-Malachi
    • Categories Constrained Nonlinear Optimization, Convex and Nonsmooth Optimization, Convex Optimization Tags , , , ,

    We present a modification of Dykstra’s algorithm which allows us to avoid projections onto general convex sets. Instead, we calculate projections onto either a halfspace or onto the intersection of two halfspaces. Convergence of the algorithm is established and special choices of the halfspaces are proposed. The option to project onto halfspaces instead of general … Read more