monte carlo simulation

Developments in mathematical algorithms and computational tools for proton CT and particle therapy treatment planning

  • Yair Censor
  • Keith E. Schubert
  • Reinhard W. Schulte
    • Categories Basic Sciences Applications, Biomedical Applications, Constrained Nonlinear Optimization Tags , , , , , , , ,

    We summarize recent results and ongoing activities in mathematical algorithms and computer science methods related to proton computed tomography (pCT) and intensitymodulated particle therapy (IMPT) treatment planning. Proton therapy necessitates a high level of delivery accuracy to exploit the selective targeting imparted by the Bragg peak. For this purpose, pCT utilizes the proton beam itself … Read more

    Optimization of noisy blackboxes with adaptive precision

  • Stéphane Alarie
  • Charles Audet
  • Pierre-Yves Bouchet
  • Sébastien Le Digabel
    • Categories Nonlinear Optimization Tags , , , , , , ,

    In derivative-free and blackbox optimization, the objective function is often evaluated through the execution of a computer program seen as a blackbox. It can be noisy, in the sense that its outputs are contaminated by random errors. Sometimes, the source of these errors is identified and controllable, in the sense that it is possible to … Read more

    Computation of exact bootstrap confidence intervals: complexity and deterministic algorithms

  • Dimitris Bertsimas
  • Bradley Sturt
    • Categories Applications - OR and Management Sciences, Approximation Algorithms, Statistics Tags , , , ,

    The bootstrap is a nonparametric approach for calculating quantities, such as confidence intervals, directly from data. Since calculating exact bootstrap quantities is believed to be intractable, randomized resampling algorithms are traditionally used. Motivated by the fact that the variability from randomization can lead to inaccurate outputs, we propose a deterministic approach. First, we establish several … Read more

    On Rates of Convergence for Stochastic Optimization Problems Under Non-I.I.D. Sampling

  • Tito Homem-de-Mello
    • Categories Optimization of Simulated Systems, Stochastic Programming Tags , , , , , ,

    In this paper we discuss the issue of solving stochastic optimization problems by means of sample average approximations. Our focus is on rates of convergence of estimators of optimal solutions and optimal values with respect to the sample size. This is a well-studied problem in case the samples are independent and identically distributed (i.e., when … Read more