Applications – Science and Engineering

Problem Formulations for Simulation-based Design Optimization using Statistical Surrogates and Direct Search

  • Michael Kokkolaras
  • Sébastien Le Digabel
  • Bastien Talgorn
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, Nonsmooth Optimization

    Typical challenges of simulation-based design optimization include unavailable gradients and unreliable approximations thereof, expensive function evaluations, numerical noise, multiple local optima and the failure of the analysis to return a value to the optimizer. One possible remedy to alleviate these issues is to use surrogate models in lieu of the computational models or simulations and … Read more

    String-Averaging Expectation-Maximization for Maximum Likelihood Estimation in Emission Tomography

  • Yair Censor
  • Álvaro Rodolfo De Pierro
  • Elias Salomão Helou
  • Tai-Been Chen
  • I-Liang Chern
  • Ming Jiang
  • Henry Horng-Shing Lu
    • Categories Biomedical Applications, Convex Optimization Tags , , , , , ,

    We study the maximum likelihood model in emission tomography and propose a new family of algorithms for its solution, called String-Averaging Expectation-Maximization (SAEM). In the String-Averaging algorithmic regime, the index set of all underlying equations is split into subsets, called “strings,” and the algorithm separately proceeds along each string, possibly in parallel. Then, the end-points … Read more

    Feasibility-Seeking and Superiorization Algorithms Applied to Inverse Treatment Planning in Radiation Therapy

  • Yair Censor
  • Ran Davidi
  • Sarah Geneser
  • Reinhard W. Schulte
  • Lei Xing
    • Categories Biomedical Applications, Convex Optimization Tags , , , ,

    We apply the recently proposed superiorization methodology (SM) to the inverse planning problem in radiation therapy. The inverse planning problem is represented here as a constrained minimization problem of the total variation (TV) of the intensity vector over a large system of linear two-sided inequalities. The SM can be viewed conceptually as lying between feasibility-seeking … Read more

    Sparsity Optimization in Design of Multidimensional Filter Networks

  • Mats Andersson
  • Oleg Burdakov
  • Hans Knutsson
  • Spartak Zikrin
    • Categories Applications - Science and Engineering, Global Optimization Applications, Multi-Criteria Optimization

    Filter networks are used as a powerful tool aimed at reducing the image processing time and maintaining high image quality. They are composed of sparse sub-filters whose high sparsity ensures fast image processing. The filter network design is related to solving a sparse optimization problem where a cardinality constraint bounds above the sparsity level. In … Read more

    A Stochastic Quasi-Newton Method for Large-Scale Optimization

  • Richard H. Byrd
  • Samantha Hansen
  • Jorge Nocedal
  • Yoram Singer
    • Categories Data-Mining, Stochastic Programming, Unconstrained Optimization Tags , , ,

    Abstract The question of how to incorporate curvature information in stochastic approximation methods is challenging. The direct application of classical quasi- Newton updating techniques for deterministic optimization leads to noisy curvature estimates that have harmful effects on the robustness of the iteration. In this paper, we propose a stochastic quasi-Newton method that is efficient, robust … Read more

    Alternating direction method of multipliers for sparse zero-variance discriminant analysis and principal component analysis

  • Brendan Ames
  • Mingyi Hong
    • Categories Data-Mining, Statistics

    We consider the task of classification in the high-dimensional setting where the number of features of the given data is significantly greater than the number of observations. To accomplish this task, we propose sparse zero-variance discriminant analysis (SZVD) as a method for simultaneouslyperforming linear discriminant analysis and feature selection on high-dimensional data. This method combines … Read more

    Subset Selection by Mallows’ Cp: A Mixed Integer Programming Approach

  • Ryuhei Miyashiro
  • Yuichi Takano
    • Categories (Mixed) Integer Nonlinear Programming, Quadratic Programming, Statistics Tags , , ,

    This paper concerns a method of selecting the best subset of explanatory variables for a linear regression model. Employing Mallows’ C_p as a goodness-of-fit measure, we formulate the subset selection problem as a mixed integer quadratic programming problem. Computational results demonstrate that our method provides the best subset of variables in a few seconds when … Read more

    Models and Solution Techniques for Production Planning Problems with Increasing Byproducts

  • Jeff Linderoth
  • James R. Luedtke
  • Srikrishna Sridhar
    • Categories Applications - OR and Management Sciences, Chemical Engineering, Facility Planning and Design Tags , ,

    We consider a production planning problem where the production process creates a mixture of desirable products and undesirable byproducts. In this production process, at any point in time the fraction of the mixture that is an undesirable byproduct increases monotonically as a function of the cumulative mixture production up to that time. The mathematical formulation … Read more

    Generalized Gauss Inequalities via Semidefinite Programming

  • Paul J. Goulart
  • Daniel Kuhn
  • Bart Paul Gerard Van Parys
    • Categories Convex Optimization, Statistics, Stochastic Programming Tags , ,

    A sharp upper bound on the probability of a random vector falling outside a polytope, based solely on the first and second moments of its distribution, can be computed efficiently using semidefinite programming. However, this Chebyshev-type bound tends to be overly conservative since it is determined by a discrete worst-case distribution. In this paper we … Read more

    Directional Sensor Control: Heuristic Approaches

  • Edwin K.P. Chong
  • Hans D Mittelmann
  • Shankarachary Ragi
    • Categories Control Applications, Meta Heuristics Tags , , ,

    We study the problem of controlling multiple 2-D directional sensors while maximizing an objective function based on the information gain corresponding to multiple target locations. We assume a joint prior Gaussian distribution for the target locations. A sensor generates a (noisy) measurement of a target only if the target lies within the field-of-view of the … Read more