concentration of measure

An analysis of the superiorization method via the principle of concentration of measure

  • Yair Censor
  • Eliahu Levy
    • Categories Constrained Nonlinear Optimization, Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , , , , , ,

    The superiorization methodology is intended to work with input data of constrained minimization problems, i.e., a target function and a constraints set. However, it is based on an antipodal way of thinking to the thinking that leads constrained minimization methods. Instead of adapting unconstrained minimization algorithms to handling constraints, it adapts feasibility-seeking algorithms to reduce … Read more

    Random projections for linear programming

  • Leo Liberti
  • Pierre-Louis Poirion
  • Ky Vu
    • Categories Linear Programming Tags , ,

    Random projections are random linear maps, sampled from appropriate distributions, that approximately preserve certain geometrical invariants so that the approximation improves as the dimension of the space grows. The well-known Johnson-Lindenstrauss lemma states that there are \LL{random matrices with surprisingly few rows} that approximately preserve pairwise Euclidean distances among a set of points. This is … Read more