Applications – Science and Engineering

Asymptotic equivalence and Kobayashi-type estimates for nonautonomous monotone operators in Banach spaces

  • Felipe Álvarez
  • Juan Peypouquet
    • Categories Basic Sciences Applications Tags , ,

    We provide a sharp generalization to the nonautonomous case of the well-known Ko\-ba\-yashi estimate for proximal iterates associated with maximal monotone operators. We then derive a bound for the distance between a continuous-in-time trajectory, namely the solution to the differential inclusion $\dot{x} + A(t)x\ni 0$, and the corresponding proximal iterations. We also establish continuity properties … Read more

    Strong asymptotic convergence of evolution equations governed by maximal monotone operators

  • Roberto Cominetti
  • Juan Peypouquet
  • S Sorin
    • Categories Applications - Science and Engineering, Convex and Nonsmooth Optimization Tags , ,

    We consider the Tikhonov-like dynamics $-\dot u(t)\in A(u(t))+\varepsilon(t)u(t)$ where $A$ is a maximal monotone operator and the parameter function $\eps(t)$ tends to 0 for $t\to\infty$ with $\int_0^\infty\eps(t)dt=\infty$. When $A$ is the subdifferential of a closed proper convex function $f$, we establish strong convergence of $u(t)$ towards the least-norm minimizer of $f$. In the general case … Read more

    General algorithmic frameworks for online problems

  • Yair Censor
  • Simeon Reich
  • Alexander J. Zaslavski
    • Categories Basic Sciences Applications, Convex Optimization Tags , , , , ,

    We study general algorithmic frameworks for online learning tasks. These include binary classification, regression, multiclass problems and cost-sensitive multiclass classification. The theorems that we present give loss bounds on the behavior of our algorithms that depend on general conditions on the iterative step sizes. CitationInternational Journal of Pure and Applied Mathematics, Vol. 46 (2008), pp. … Read more

    Passenger Name Record Data Mining Based Cancellation Forecasting for Revenue Management

  • Dolores Romero Morales
  • Jingbo Wang
    • Categories Data-Mining, Yield Management Tags , , , ,

    Revenue management (RM) enhances the revenues of a company by means of demand-management decisions. An RM system must take into account the possibility that a booking may be canceled, or that a booked customer may fail to show up at the time of service (no-show). We review the Passenger Name Record data mining based cancellation … Read more

    Accelerated line-search and trust-region methods

  • Pierre-Antoine Absil
  • Kyle A. Gallivan
    • Categories Applications - Science and Engineering, Unconstrained Optimization Tags , , ,

    In numerical optimization, line-search and trust-region methods are two important classes of descent schemes, with well-understood global convergence properties. Here we consider “accelerated” versions of these methods, where the conventional iterate is allowed to be replaced by any point that produces at least as much decrease in the cost function as a fixed fraction of … Read more

    Concave programming for minimizing the zero-norm over polyhedral sets

  • Francesco Rinaldi
  • Fabio Schoen
  • Marco Sciandrone
    • Categories Constrained Nonlinear Optimization, Data-Mining Tags , ,

    Given a non empty polyhedral set, we consider the problem of finding a vector belonging to it and having the minimum number of nonzero components, i.e., a feasible vector with minimum zero-norm. This nonsmooth combinatorial optimization problem is NP-Hard and arises in various fields such as machine learning, pattern recognition, signal processing. We propose two … Read more

    Water Network Design by MINLP

  • Cristiana Bragalli
  • Claudia D'Ambrosio
  • Jon Lee
  • Andrea Lodi
  • Paolo Toth
    • Categories (Mixed) Integer Nonlinear Programming, Civil and Environmental Engineering

    We propose a solution method for a water-network optimization problem using a nonconvex continuous NLP (nonlinear programming) relaxation and a MINLP (mixed integer nonlinear programming) search. Our approach employs a relatively simple and accurate model that pays some attention to the requirements of the solvers that we employ. Our view is that in doing so, … Read more

    A conjugate-gradient based approach for approximate solutions of quadratic programs

  • Fredrik Carlsson
  • Anders Forsgren
    • Categories Biomedical Applications, Quadratic Programming Tags , , ,

    This paper deals with numerical behaviour and convergence properties of a recently presented column generation approach for optimization of so called step-and-shoot radiotherapy treatment plans. The approach and variants of it have been reported to be efficient in practice, finding near-optimal solutions by generating only a low number of columns. The impact of different restrictions … Read more