Applications – Science and Engineering

Continuous optimization of beamlet intensities for photon and proton radiotherapy

  • M. Alber
  • R. Reemtsen
    • Categories Biomedical Applications Tags , , , , , , , ,

    Inverse approaches and, in particular, intensity modulated radiotherapy (IMRT), in combination with the development of new technologies such as multi-leaf collimators (MLCs), have enabled new potentialities of radiotherapy for cancer treatment. The main mathematical tool needed in this connection is numerical optimization. In this article, the variety of continuous optimization approaches, which have been proposed … Read more

    Computational experience with an interior point algorithm for large scale contact problems

  • Dominikus Noll
  • Y. Renard
  • G. Tanoh
    • Categories Constrained Nonlinear Optimization, Mechanical Engineering, Quadratic Programming Tags , , ,

    In this paper we present an interior point method for large scale Signorini elastic contact problems. We study the case of an elastic body in frictionless contact with a rigid foundation. Primal and primal-dual algorithms are developed to solve the quadratic optimization problem arising in the variational formulation. Our computational study confirms the efficiency of … Read more

    A Tabu Search Algorithm for Partitioning

  • Alex Murillo
  • Eduardo Piza
  • Javier Trejos
    • Categories Data-Mining, Meta Heuristics, Statistics Tags , , ,

    We present an original method for partitioning by automatic classi- fication, using the optimization technique of tabu search. The method uses a classical tabu search scheme based on transfers for the minimization of the within variance; it introduces in the tabu list the indicator of the object transfered. This method is compared with two stochastic … Read more

    Convergent relaxations of polynomial matrix inequalities and static output feedback

  • Didier Henrion
  • Jean-Bernard Lasserre
    • Categories Control Applications, Semi-definite Programming Tags , , ,

    Using a moment interpretation of recent results on sum-of-squares decompositions of non-negative polynomial matrices, we propose a hierarchy of convex linear matrix inequality (LMI) relaxations to solve non-convex polynomial matrix inequality (PMI) optimization problems, including bilinear matrix inequality (BMI) problems. This hierarchy of LMI relaxations generates a monotone sequence of lower bounds that converges to … Read more

    A Mixed-Integer Programming Approach to Multi-Class Data Classification Problem

  • Metin Turkay
  • Fadime Uney
    • Categories (Mixed) Integer Linear Programming, Data-Mining Tags , , ,

    This paper presents a new data classification method based on mixed-integer programming. Traditional approaches that are based on partitioning the data sets into two groups perform poorly for multi-class data classification problems. The proposed approach is based on the use of hyper-boxes for defining boundaries of the classes that include all or some of the … Read more

    The Design and Implementation of a Generic Sparse Bundle Adjustment Software Package Based on the Levenberg-Marquardt Algorithm

  • Antonis Argyros
  • Manolis Lourakis
    • Categories Basic Sciences Applications, Nonlinear Systems and Least-Squares, Optimization Software and Modeling Systems Tags , , , , ,

    Bundle adjustment using the Levenberg-Marquardt minimization algorithm is almost invariably used as the last step of every feature-based structure and motion estimation computer vision algorithm to obtain optimal 3D structure and viewing parameter estimates. However, due to the large number of unknowns contributing to the minimized reprojection error, a general purpose implementation of the Levenberg-Marquardt … Read more

    Optimal Nodal Control of Networked Hyperbolic Systems: Evaluation of Derivatives

  • Martin Gugat
    • Categories Applications - Science and Engineering, Control Applications, Optimization of Systems modeled by PDEs Tags , , , , ,

    We consider a networked system defined on a graph where each edge corresponds to a quasilinear hyperbolic system with space dimension one. At the nodes, the system is governed by algebraic node conditions. The system is controlled at the nodes of the graph. Optimal control problems for systems of this type arise in the operation … Read more

    Optimal distance separating halfspace

  • Emilio Carrizosa
  • Frank Plastria
    • Categories Data-Mining, Global Optimization Applications Tags , ,

    One recently proposed criterion to separate two datasets in discriminant analysis, is to use a hyperplane which minimises the sum of distances to it from all the misclassified data points. Here all distances are supposed to be measured by way of some fixed norm,while misclassification means lying on the wrong side of the hyperplane, or … Read more

    Optimal expected-distance separating halfspace

  • Emilio Carrizosa
  • Frank Plastria
    • Categories Data-Mining, Global Optimization Applications, Statistics Tags , ,

    One recently proposed criterion to separate two datasets in discriminant analysis, is to use a hyperplane which minimises the sum of distances to it from all the misclassified data points. Here all distances are supposed to be measured by way of some fixed norm, while misclassification means lying on the wrong side of the hyperplane, … Read more

    A survey of the S-lemma

  • Imre Pólik
  • Tamás Terlaky
    • Categories Control Applications, Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , , , , , ,

    In this survey we review the many faces of the S-lemma, a result about the correctness of the S-procedure. The basic idea of this widely used method came from control theory but it has important consequences in quadratic and semidefinite optimization, convex geometry and linear algebra as well. These were active research areas, but as … Read more