Effective Strategies to Teach Operations Research to Non-Mathematics Majors

  • Somayeh Moazeni
    • Categories Basic Sciences Applications, Other Topics Tags

    Operations Research (OR) is the discipline of applying advanced analytical methods to help make better decisions (Horner (2003)). OR is characterized by its broad applicability and its interdisciplinary nature. Currently, in addition to mathematics, many other undergraduate programs such as management sciences, business, economics, electrical engineering, civil engineering, chemical engineering, and related fields, have incorporated … Read more

    POST-PARETO ANALYSIS FOR MULTIOBJECTIVE PARABOLIC CONTROL SYSTEMS

  • Henri Bonnel
    • Categories Distributed Control, Multi-Criteria Optimization Tags , , , ,

    In this paper is presented the problem of optimizing a functional over a Pareto control set associated with a convex multiobjective control problem in Hilbert spaces, namely parabolic system. This approach generalizes for this setting some results obtained in finite dimensions. Some examples are presented. General optimality results are obtained, and a special attention is … Read more

    Superiorization: An optimization heuristic for medical physics

  • Yair Censor
  • Ran Davidi
  • Edgar Garduño
  • Gabor T. Herman
    • Categories Biomedical Applications, Constrained Nonlinear Optimization Tags , , , ,

    Purpose: To describe and mathematically validate the superiorization methodology, which is a recently-developed heuristic approach to optimization, and to discuss its applicability to medical physics problem formulations that specify the desired solution (of physically given or otherwise obtained constraints) by an optimization criterion. Methods: The superiorization methodology is presented as a heuristic solver for a … Read more

    A first-order block-decomposition method for solving two-easy-block structured semidefinite programs

  • Renato D.C. Monteiro
  • Camilo Ortiz
  • Benar Fux Svaiter
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming, Optimization Software Benchmark Tags , , , , , ,

    In this paper, we consider a first-order block-decomposition method for minimizing the sum of a convex differentiable function with Lipschitz continuous gradient, and two other proper closed convex (possibly, nonsmooth) functions with easily computable resolvents. The method presented contains two important ingredients from a computational point of view, namely: an adaptive choice of stepsize for … Read more

    Optimality, identifiability, and sensitivity

  • Dmitriy Drusvyatskiy
  • Adrian Lewis
    • Categories Nonsmooth Optimization Tags , , , , , , , , ,

    Around a solution of an optimization problem, an “identifiable” subset of the feasible region is one containing all nearby solutions after small perturbations to the problem. A quest for only the most essential ingredients of sensitivity analysis leads us to consider identifiable sets that are “minimal”. This new notion lays a broad and intuitive variational-analytic … Read more

    Mixed Integer Linear Programming Formulation Techniques

  • Juan Pablo Vielma
    • Categories (Mixed) Integer Linear Programming

    A wide range of problems can be modeled as Mixed Integer Linear Programming (MIP) problems using standard formulation techniques. However, in some cases the resulting MIP can be either too weak or too large to be effectively solved by state of the art solvers. In this survey we review advanced MIP formulation techniques that result … Read more

    Stochastic optimization and sparse statistical recovery: An optimal algorithm for high dimensions

  • Alekh Agarwal
  • Martin J Wainwright
  • Sahand Negahban
    • Categories Convex Optimization, Stochastic Programming Tags , ,

    We develop and analyze stochastic optimization algorithms for problems in which the expected loss is strongly convex, and the optimum is (approximately) sparse. Previous approaches are able to exploit only one of these two structures, yielding an $\order(\pdim/T)$ convergence rate for strongly convex objectives in $\pdim$ dimensions, and an $\order(\sqrt{(\spindex \log \pdim)/T})$ convergence rate when … Read more