Applications – Science and Engineering

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

    Model Problems for the Multigrid Optimization of Systems Governed by Differential Equations

  • Robert Michael Lewis
  • Stephen G. Nash
    • Categories Infinite Dimensional Optimization, Optimization of Systems modeled by PDEs, Systems governed by Differential Equations Optimization Tags ,

    We present a multigrid approach to the optimization of systems governed by differential equations. Such optimization problems have many applications, and are a broader class of problems than systems of equations. Using several model problems we give evidence (both theoretical and numerical) that a multigrid approach can often be successful in the setting of optimization. … Read more

    Efficient Algorithms for Large Scale Global Optimization: Lennard-Jones clusters

  • Marco Locatelli
  • Fabio Schoen
    • Categories Chemical Engineering, Stochastic Approaches Tags , , , , ,

    A standard stochastic global optimization method is applied to the challenging problem of finding the minimum energy conformation of cluster of identical atoms interacting through the Lennard-Jones potential. The method proposed is based on the use of a two-phase local search procedure which is capable of significantly enlarge the basin of attraction of the global … Read more

    Pattern Search Methods for User-Provided Points:Application to Molecular Geometry Problems

  • Pedro Alberto
  • Luis Nunes Vicente
  • Fernando Nogueira
  • Humberto Rocha
    • Categories Basic Sciences Applications, Unconstrained Optimization Tags , , , , ,

    This paper deals with the application of pattern search methods to the numerical solution of a class of molecular geometry problems with important applications in molecular physics and chemistry. The goal is to find a configuration of a cluster or a molecule with minimum total energy. The minimization problems in this class of geometry molecular … Read more

    PENNON – A Code for Convex Nonlinear and Semidefinite Programming

  • Michal Kočvara
  • Michael Stingl
    • Categories Convex Optimization, Mechanical Engineering, Semi-definite Programming

    We introduce a computer program PENNON for the solution of problems of convex Nonlinear and Semidefinite Programming (NLP-SDP). The algorithm used in PENNON is a generalized version of the Augmented Lagrangian method, originally introduced by Ben-Tal and Zibulevsky for convex NLP problems. We present generalization of this algorithm to convex NLP-SDP problems, as implemented in … Read more

    A binary LP model to the facility layout problem

  • Christos Papahristodoulou
    • Categories 0-1 Programming, Applications - OR and Management Sciences, Facility Planning and Design Tags , , , ,

    In facility layout problems, a major concern is the optimal design or remodeling of the facilities of an organization. The decision-maker’s objective is to arrange the facility in an optimal way, so that the interaction among functions (i.e. machines, inventories, persons) and places (i.e. offices, work locations, depots) is efficient. A simple pure-binary LP model … Read more

    The least-intensity feasible solution for aperture-based inverse planning in radiation therapy.

  • Yair Censor
  • James M. Galvin
  • Darek Michalski
  • Ying Xiao
    • Categories Biomedical Applications, Convex Optimization, Nonlinear Systems and Least-Squares Tags , , , , ,

    Aperture-based inverse planning (ABIP) for intensity modulated radiation therapy (IMRT) treatment planning starts with external radiation fields (beams) that fully conform to the target(s) and then superimposes sub-fields called segments to achieve complex shaping of 3D dose distributions. The segments’ intensities are determined by solving a feasibility problem. The least-intensity feasible (LIF) solution, proposed and … Read more

    A New Mathematical-Programming Framework for Facility-Layout Design

  • Miguel F. Anjos
  • Anthony Vannelli
    • Categories Applications - OR and Management Sciences, Multidisciplinary Design Optimization, VLSI layout Tags , , ,

    We present a new framework for efficiently finding competitive solutions for the facility-layout problem. This framework is based on the combination of two new mathematical-programming models. The first model is a relaxation of the layout problem and is intended to find good starting points for the iterative algorithm used to solve the second model. The … Read more