superiorization method

Per-RMAP: Feasibility-Seeking and Superiorization Methods for Floorplanning with I/O Assignment

  • ShanYu
  • Yair Censor
  • Ming Jiang
  • Guojie Luo
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, VLSI layout Tags , , , ,

    The feasibility-seeking approach provides a systematic scheme to manage and solve complex constraints for continuous problems, and we explore it for the floorplanning problems with increasingly heterogeneous constraints. The classic legality constraints can be formulated as the union of convex sets. However, the convergence of conventional projection-based algorithms is not guaranteed when the constraints sets … Read more

    Superiorization as a novel strategy for linearly constrained inverse radiotherapy treatment planning

  • Florian Barkmann
  • Yair Censor
  • Niklas Wahl
    • Categories Biomedical Applications, Constrained Nonlinear Optimization, Convex Optimization Tags , , , , , ,

    Objective: We apply the superiorization methodology to the intensity-modulated radiation therapy (IMRT) treatment planning problem. In superiorization, linear voxel dose inequality constraints are the fundamental modeling tool within which a feasibility-seeking projection algorithm will seek a feasible point. This algorithm is then perturbed with gradient descent steps to reduce a nonlinear objective function. Approach: Within … 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

    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