Linear-quadratic control problem with a linear term on semiinfinite interval:theory and applications

  • Leonid Faybusovich
  • Thanasak Mouktonglang
    • Categories Control Applications, Infinite Dimensional Optimization, Multi-Criteria Optimization Tags , ,

    We describe a complete solution of the linear-quaratic control problem with the linear term in the objective function on a semiinfinite interval. This problem has important applications to calculation of Nesterov-Todd and other primal-dual directions in infinite-dimensional setting. Citation Technical report, University of Notre Dame, December, 2003 Article Download View Linear-quadratic control problem with a … Read more

    The dose-volume constraint satisfaction problem for inverse treatment planning with field segments

  • Yair Censor
  • James M. Galvin
  • Darek Michalski
  • Ying Xiao
    • Categories Biomedical Applications Tags , ,

    The prescribed goals of radiation treatment planning are often expressed in terms of dose-volume constraints. We present a novel formulation of a dose-volume constraint satisfaction search for the discretized radiation therapy model. This approach does not rely on any explicit cost function. The inverse treatment planning uses the aperture based approach with predefined, according to … Read more

    Transfer function restoration in 3D electron microscopy via iterative data refinement

  • J.M. Carazo
  • Yair Censor
  • C.O.S. Sorzano
  • Gabor T. Herman
  • R. Marabini
    • Categories Biomedical Applications Tags , ,

    Three-dimensional electron microscopy (3D-EM) is a powerful tool for visualizing complex biological systems. As any other imaging device, the electron microscope introduces a transfer function (called in this field the Contrast Transfer Function, CTF) into the image acquisition process that modulates the various frequencies of the signal. Thus, 3D reconstructions performed with these CTF-affected projections … Read more

    On an Approximation of the Hessian of the Lagrangian

  • Florian Jarre
    • Categories Constrained Nonlinear Optimization, Optimization Software Design Principles Tags , ,

    In the context of SQP methods or, more recently, of sequential semidefinite programming methods, it is common practice to construct a positive semidefinite approximation of the Hessian of the Lagrangian. The Hessian of the augmented Lagrangian is a suitable approximation as it maintains local superlinear convergence under appropriate assumptions. In this note we give a … Read more

    A Polytope for a Product of Real Linear Functions in 0/1 Variables

  • Don Coppersmith
  • Oktay Gunluk
  • Jon Lee
  • Janny Leung
    • Categories 0-1 Programming Tags ,

    In the context of integer programming, we develop a polyhedral method for linearizing a product of a pair of real linear functions in 0/1 variables. As an example, by writing a pair of integer variables in binary expansion, we have a technique for linearizing their product. We give a complete linear description for the resulting … Read more

    Weak Stationarity: Eliminating the Gap between Necessary and Sufficient Conditions

  • Alexander Y. Kruger
    • Categories Nonsmooth Optimization Tags , , , , ,

    Starting from known necessary extremality conditions in terms of strict subdifferentials and normals the notion of weak stationarity is introduced. It is defined in terms of initial space elements. The necessary conditions become necessary and sufficient (for stationarity). Citation School of Information Technology and Mathematical Sciences, Centre of Information and Applied Optimization, University of Ballarat, … Read more

    Boundedness Theorems for the Relaxation Method

  • Edoardo Amaldi
  • Raphael Hauser
    • Categories Linear Programming, Polyhedra Tags , , ,

    A classical theorem by Block and Levin says that certain variants of the relaxation method for solving systems of linear inequalities produce bounded sequences of intermediate solutions even when running on inconsistent input data. Using a new approach, we prove a more general version of this result and answer an old open problem of quantifying … Read more

    Some Properties of Regularization and Penalization Schemes for MPECs

  • Daniel Ralph
  • Stephen Wright
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags , ,

    Some properties of regularized and penalized nonlinear programming formulations of mathematical programs with equilibrium constraints (MPECs) are described. The focus is on the properties of these formulations near a local solution of the MPEC at which strong stationarity and a second-order sufficient condition are satisfied. In the regularized formulations, the complementarity condition is replaced by … Read more

    Solving the Hub Location Problem with Modular Link Capacities

  • Giuliana Carello
  • Hande Yaman
    • Categories Branch and Cut Algorithms, Meta Heuristics, Telecommunications Tags , ,

    This paper deals with a capacitated hub location problem arising in the design of telecommunications networks. The problem is different from the classical hub location problem in two ways: the cost of using an edge is not linear but stepwise and the capacity of an hub restricts the amount of traffic transiting through the hub … Read more