Yair Censor

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

Feasibility-Seeking and Superiorization Algorithms Applied to Inverse Treatment Planning in Radiation Therapy

  • Yair Censor
  • Ran Davidi
  • Sarah Geneser
  • Reinhard W. Schulte
  • Lei Xing
    • Categories Biomedical Applications, Convex Optimization Tags , , , ,

    We apply the recently proposed superiorization methodology (SM) to the inverse planning problem in radiation therapy. The inverse planning problem is represented here as a constrained minimization problem of the total variation (TV) of the intensity vector over a large system of linear two-sided inequalities. The SM can be viewed conceptually as lying between feasibility-seeking … Read more

    String-Averaging Projected Subgradient Methods for Constrained Minimization

  • Yair Censor
  • Alexander J. Zaslavski
    • Categories Constrained Nonlinear Optimization, Convex Optimization Tags , , , , , , , , ,

    We consider constrained minimization problems and propose to replace the projection onto the entire feasible region, required in the Projected Subgradient Method (PSM), by projections onto the individual sets whose intersection forms the entire feasible region. Specifically, we propose to perform such projections onto the individual sets in an algorithmic regime of a feasibility-seeking iterative … Read more

    Cooperative Wireless Sensor Network Positioning via Implicit Convex Feasibility

  • Yair Censor
  • Mohammad R. Gholami
  • Erik G. Strom
  • Luba Tetruashvili
    • Categories Facility Planning and Design, Nonlinear Optimization Tags , , , ,

    We propose a distributed positioning algorithm to estimate the unknown positions of a number of target nodes, given distance measurements between target nodes and between target nodes and a number of reference nodes at known positions. Based on a geometric interpretation, we formulate the positioning problem as an implicit convex feasibility problem in which some … Read more

    Projected subgradient minimization versus superiorization

  • Yair Censor
  • Ran Davidi
  • Gabor T. Herman
  • Reinhard W. Schulte
  • Luba Tetruashvili
    • Categories Biomedical Applications, Constrained Nonlinear Optimization Tags , , , , , , , ,

    The projected subgradient method for constrained minimization repeatedly interlaces subgradient steps for the objective function with projections onto the feasible region, which is the intersection of closed and convex constraints sets, to regain feasibility. The latter poses a computational difficulty and, therefore, the projected subgradient method is applicable only when the feasible region is “simple … Read more

    Family Constraining of Iterative Algorithms

  • Yair Censor
  • Ioana Pantelimon
  • Constantin Popa
    • Categories Applications - Science and Engineering, Nonlinear Systems and Least-Squares Tags , ,

    In constraining iterative processes, the algorithmic operator of the iterative process is pre-multiplied by a constraining operator at each iterative step. This enables the constrained algorithm, besides solving the original problem, also to find a solution that incorporates some prior knowledge about the solution. This approach has been useful in image restoration and other image … Read more

    Superiorization: An optimization heuristic for medical physics

  • Yair Censor
  • Ran Davidi
  • Edgar Garduño
  • Gabor T. Herman
    • Categories Biomedical Applications, Constrained Nonlinear Optimization Tags , , , ,

    Purpose: To describe and mathematically validate the superiorization methodology, which is a recently-developed heuristic approach to optimization, and to discuss its applicability to medical physics problem formulations that specify the desired solution (of physically given or otherwise obtained constraints) by an optimization criterion. Methods: The superiorization methodology is presented as a heuristic solver for a … Read more

    Convergence and Perturbation Resilience of Dynamic String-Averaging Projection Methods

  • Yair Censor
  • Alexander J. Zaslavski
    • Categories Biomedical Applications, Convex Optimization, Parallel Algorithms Tags , , , , , , , , ,

    We consider the convex feasibility problem (CFP) in Hilbert space and concentrate on the study of string-averaging projection (SAP) methods for the CFP, analyzing their convergence and their perturbation resilience. In the past, SAP methods were formulated with a single predetermined set of strings and a single predetermined set of weights. Here we extend the … Read more

    Extrapolation and Local Acceleration of an Iterative Process for Common Fixed Point Problems

  • Andrzej Cegielski
  • Yair Censor
    • Categories Convex Optimization Tags , , , ,

    We consider sequential iterative processes for the common fixed point problem of families of cutter operators on a Hilbert space. These are operators that have the property that, for any point x∈H, the hyperplane through Tx whose normal is x-Tx always “cuts” the space into two half-spaces one of which contains the point x while … Read more

    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