Applications – Science and Engineering

Socially optimal location of facilities with fixed servers, stochastic demand and congestion

  • Ignacio Castillo
  • Armann Ingolfsson
  • Thaddeus Sim
    • Categories (Mixed) Integer Nonlinear Programming, Multidisciplinary Design Optimization

    We present two capacity choice scenarios for the socially optimal location of facilities with fixed servers, stochastic demand and congestion. Walk-in health clinics, motor vehicle inspection stations, automobile emissions testing stations, and internal service systems are motivating examples of such facilities. The choice of locations for such facilities influences not only distances for users traveling … Read more

    RIOTS_95–a MATLAB Toolbox for Solving General Optimal Control Problems And Its Applications to Chemical Processes

  • YangQuan Chen
  • Adam L. Schwartz
    • Categories Chemical Engineering, Problem Solving Environments, Systems governed by Differential Equations Optimization Tags , , , , ,

    RIOTS_95 is a group of programs and utilities, written mostly in C, Fortran and M-file scripts and designed as a toolbox for MATLAB, that provides an interactive environment for solving a very broad class of optimal control problems (OCP’s). RIOTS_95 comes pre-compiled for use with the Windows 95/98/2000 or Windows NT operating systems. The user’s … Read more

    Nonlinear Optimisation in CHP-Applications

  • Wilhelm Althaus
  • Michael Lucht
  • Michael Wigbels
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , ,

    At the Fraunhofer Institute UMSICHT a nonlinear model has been developed facilitating the dynamic optimisation of combined heat and power production systems. The strategy called “dynamic supply temperature optimisation” is a very promising approach to use the DH-network itself as a large heat storage causing no additional investment cost. The pipeline system of a district … Read more

    Optimal Magnetic Shield Design with Second-Order Cone Programming

  • Takashi Sasakawa
  • Takashi Tsuchiya
    • Categories Multidisciplinary Design Optimization, Second-Order Cone Programming Tags , , ,

    In this paper, we consider a continuous version of the convex network flow problem which involves the integral of the Euclidean norm of the flow and its square in the objective function. A discretized version of this problem can be cast as a second-order cone program, for which efficient primal-dual interior-point algorithms have been developed … Read more

    The Thirteen Spheres: A New Proof

  • Kurt M. Anstreicher
    • Categories Basic Sciences Applications Tags , , ,

    The “thirteen spheres problem”, also known as the “Gregory-Newton problem” is to determine the maximum number of three-dimensional spheres that can simultaneously touch a given sphere, where all the spheres have the same radius. The history of the problem goes back to a disagreement between Isaac Newton and David Gregory in 1694. Using a combination … Read more

    Robust regularization

  • Adrian Lewis
    • Categories Control Applications, Nonsmooth Optimization, Robust Optimization Tags , , , , , , , ,

    Given a real function on a Euclidean space, we consider its “robust regularization”: the value of this new function at any given point is the maximum value of the original function in a fixed neighbourhood of the point in question. This construction allows us to impose constraints in an optimization problem *robustly*, safeguarding a constraint … Read more

    Global and Convex Optimization in Modeling Environments: Compiler-Based, Excel, and Mathematica Implementations

  • János Pintér
    • Categories Applications - Science and Engineering, Global Optimization, Optimization Software and Modeling Systems

    We present a review of several software products that serve to analyze and solve nonlinear (specifically including global) optimization problems across different hardware and software platforms. The implementations discussed are LGO, as a stand-alone, but compiler-dependent modeling and solver environment; its Excel platform implementation; and MathOptimizer, a native solver package for Mathematica users. The discussion … Read more

    Nonlinear Model Predictive Control via Feasibility-Perturbed Sequential Quadratic Programming

  • J B Rawlings
  • M. J. Tenny
  • Stephen Wright
    • Categories Chemical Engineering, Constrained Nonlinear Optimization, Control Applications Tags , ,

    Model predictive control requires the solution of a sequence of continuous optimization problems that are nonlinear if a nonlinear model is used for the plant. We describe briefly a trust-region feasibility-perturbed sequential quadratic programming algorithm (developed in a companion report), then discuss its adaptation to the problems arising in nonlinear model predictive control. Computational experience … Read more

    Distance Weighted Discrimination

  • J. S. Marron
  • Michael J. Todd
    • Categories Second-Order Cone Programming, Statistics Tags ,

    High Dimension Low Sample Size statistical analysis is becoming increasingly important in a wide range of applied contexts. In such situations, it is seen that the popular Support Vector Machine suffers from “data piling” at the margin, which can diminish generalizability. This leads naturally to the development of Distance Weighted Discrimination, which is based on … Read more

    TfMin: Short Reference Manual

  • Jean-Baptiste Caillau
  • Joseph Noailles
  • Joseph Gergaud
    • Categories Control Applications Tags , , ,

    This is a short guide to use the Fortran and Matlab package TfMin designed for the numerical solution of continuous 3D minimum-time orbit transfer around the Earth (with free final longitude), especially for low thrust engines. The underlying method is single shooting. The Matlab interface with the solver allows the user to define the problem … Read more