Yair Censor

Bio-sketch and research interests appear at: http://math.haifa.ac.il/YAIR/censor-interests.html

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

    On linear infeasibility arising in intensity-modulated radiation therapy inverse planning

  • Adi Ben-Israel
  • Yair Censor
  • James M. Galvin
  • Ying Xiao
    • Categories Applications - Science and Engineering, Approximation Algorithms Tags , , , , ,

    Intensity–modulated radiation therapy (IMRT) gives rise to systems of linear inequalities, representing the effects of radiation on the irradiated body. These systems are often infeasible, in which case one settles for an approximate solution, such as an {a,ß}–relaxation, meaning that no more than a percent of the inequalities are violated by no more than ß … Read more

    On diagonally-relaxed orthogonal projection methods

  • Yair Censor
  • Tommy Elfving
  • Gabor T. Herman
  • Touraj Nikazad
    • Categories Biomedical Applications, Unconstrained Optimization Tags , , , ,

    We propose and study a block-iterative projections method for solving linear equations and/or inequalities. The method allows diagonal component-wise relaxation in conjunction with orthogonal projections onto the individual hyperplanes of the system, and is thus called diagonally-relaxed orthogonal projections (DROP). Diagonal relaxation has proven useful in accelerating the initial convergence of simultaneous and block-iterative projection … Read more

    Perturbed projections and subgradient projections for the multiple-sets split feasibility problem

  • Yair Censor
  • Avi Motova
  • Alexander Segal
    • Categories Convex and Nonsmooth Optimization, Unconstrained Optimization

    We study the multiple-sets split feasibility problem that requires to find a point closest to a family of closed convex sets in one space such that its image under a linear transformation will be closest to another family of closed convex sets in the image space. By casting the problem into an equivalent problem in … Read more

    A unified approach for inversion problems in intensity-modulated radiation therapy

  • Thomas Bortfeld
  • Yair Censor
  • Benjamin Martin
  • Alexei Trofimov
    • Categories Biomedical Applications, Nonlinear Optimization

    We propose and study a unified model for handling dose constraints (physical dose, equivalent uniform dose (EUD), etc.) and radiation source constraints in a single mathematical framework based on the split feasibility problem. The model does not impose on the constraints an exogenous objective (merit) function. The optimization algorithm minimizes a weighted proximity function that … Read more

    The Application of an Oblique-Projected Landweber Method to a Model of Supervised Learning

  • Yair Censor
  • Tommy Elfving
  • Per-Erik Forssen
  • Gosta Granlund
  • Bjorn Johansson
  • Vladimir Kozlov
    • Categories Applications - Science and Engineering Tags , , , ,

    This paper brings together a novel information representation model for use in signal processing and computer vision problems, with a particular algorithmic development of the Landweber iterative algorithm. The information representation model allows a representation of multiple values for a variable as well as expression of confidence. Both properties are important for effective computation using … Read more

    The multiple-sets split feasibility problem and its applications for inverse problems

  • Thomas Bortfeld
  • Yair Censor
  • Tommy Elfving
  • Nirit Kopf
    • Categories Applications - Science and Engineering, Biomedical Applications, Convex Optimization

    The multiple-sets split feasibility problem requires to find a point closest to a family of closed convex sets in one space such that its image under a linear transformation will be closest to another family of closed convex sets in the image space. It can be a model for many inverse problems where constraints are … Read more

    Computational acceleration of projection algorithms for the linear best approximation problem

  • Yair Censor
    • Categories Convex Optimization

    This is an experimental computational account of projection algorithms for the linear best approximation problem. We focus on the sequential and simultaneous versions of Dykstra’s algorithm and the Halpern-Lions-Wittmann-Bauschke algorithm for the best approximation problem from a point to the intersection of closed convex sets in the Euclidean space. These algorithms employ different iterative approaches … Read more

    Algorithms for the quasiconvex feasibility problem

  • Yair Censor
  • Alexander Segal
    • Categories Convex and Nonsmooth Optimization Tags , , , , ,

    We study the behavior of subgradient projection algorithms for the quasiconvex feasibility problem of finding a point x^* in R^n that satisfies the inequalities f_i(x^*) less or equal 0, for all i=1,2,…,m, where all functions are continuous and quasiconvex. We consider the consistent case when the solution set is nonempty. Since the Fenchel-Moreau subdifferential might … Read more

    Best approximation to common fixed points of a semigroup of nonexpansive operators

  • Arkady Aleyner
  • Yair Censor
    • Categories Constrained Nonlinear Optimization, Convex and Nonsmooth Optimization Tags , , , ,

    We study a sequential algorithm for finding the projection of a given point onto the common fixed points set of a semigroup of nonexpansive operators in Hilbert space. The convergence of such an algorithm was previously established only for finitely many nonexpansive operators. Algorithms of this kind have been applied to the best approximation and … Read more