projection methods

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

    Mathematical optimization for the inverse problem of intensity modulated radiation therapy

  • Yair Censor
    • Categories Biomedical Applications, Global Optimization Applications Tags , , , , ,

    In this tutorial we discuss modeling issues in intensity modulated radiation therapy, contrasting the continuous model with the fully-discretized one and considering feasibility formulations versus optimization setups. We review briefly some mathematical optimization techniques for IMRT. These include global optimization, multi-objective optimization, linear and mixed integer programming and projection methods. Citation in: J.R. Palta and … Read more

    The method of reflection-projection for convex feasibility problems with an obtuse cone

  • Heinz Bauschke
  • Serge Kruk
    • Categories Convex Optimization, Linear Programming Tags , , ,

    The convex feasibility problem asks to find a point in the intersection of finitely many closed convex sets in Euclidean space. This problem is of fundamental importance in mathematics and physical sciences, and it can be solved algorithmically by the classical method of cyclic projections. In this paper, the case where one of the constraints … Read more