projection algorithms

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

    Conditional Extragradient Algorithms for Solving Constrained Variational Inequalities

  • Yunier Bello-Cruz
  • R. Diaz Millan
  • Hung M. Phan
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization, Global Optimization Tags , ,

    In this paper, we generalize the classical extragradient algorithm for solving variational inequality problems by utilizing non-null normal vectors of the feasible set. In particular, conceptual algorithms are proposed with two different linesearches. We then establish convergence results for these algorithms under mild assumptions. Our study suggests that non-null normal vectors may significantly improve convergence … Read more

    A new class of potential affine algorithms for linear convex programming

  • A. W. Martins Pinto
  • Paulo Roberto Oliveira
  • J. X. da Cruz Neto
    • Categories Convex Optimization Tags ,

    We obtain a new class of primal affine algorithms for the linearly constrained convex programming. It is constructed from a family of metrics generated the r power, r>=1, of the diagonal iterate vector matrix. We obtain the so called weak convergence. That class contains, as particular cases, the multiplicative Eggermont algorithm for the minimization of … Read more

    The least-intensity feasible solution for aperture-based inverse planning in radiation therapy.

  • Yair Censor
  • James M. Galvin
  • Darek Michalski
  • Ying Xiao
    • Categories Biomedical Applications, Convex Optimization, Nonlinear Systems and Least-Squares Tags , , , , ,

    Aperture-based inverse planning (ABIP) for intensity modulated radiation therapy (IMRT) treatment planning starts with external radiation fields (beams) that fully conform to the target(s) and then superimposes sub-fields called segments to achieve complex shaping of 3D dose distributions. The segments’ intensities are determined by solving a feasibility problem. The least-intensity feasible (LIF) solution, proposed and … Read more

    Block-Iterative Algorithms with Underrelaxed Bregman Projections

  • Yair Censor
  • Gabor T. Herman
    • Categories Constrained Nonlinear Optimization, Convex Optimization Tags , , , ,

    The notion of relaxation is well understood for orthogonal projections onto convex sets. For general Bregman projections it was considered only for hyperplanes and the question of how to relax Bregman projections onto convex sets that are not linear (i.e., not hyperplanes or half-spaces) has remained open. A definition of underrelaxation of Bregman projections onto … Read more