Basic Sciences Applications

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

    Asymptotic almost-equivalence of abstract evolution systems

  • Felipe Álvarez
  • Juan Peypouquet
    • Categories Basic Sciences Applications, Convex and Nonsmooth Optimization Tags , ,

    We study the asymptotic behavior of almost-orbits of abstract evolution systems in Banach spaces with or without a Lipschitz assumption. In particular, we establish convergence, convergence in average and almost-convergence of almost-orbits both for the weak and the strong topologies based on the behavior of the orbits. We also analyze the set of almost-stationary points. … 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. Citation International Journal of Pure and Applied Mathematics, Vol. 46 (2008), … Read more

    Probing the Pareto frontier for basis pursuit solutions

  • Michael P. Friedlander
  • Ewout van den Berg
    • Categories Basic Sciences Applications, Convex Optimization Tags , , , , , , ,

    The basis pursuit problem seeks a minimum one-norm solution of an underdetermined least-squares problem. Basis pursuit denoise (BPDN) fits the least-squares problem only approximately, and a single parameter determines a curve that traces the optimal trade-off between the least-squares fit and the one-norm of the solution. We prove that this curve is convex and continuously … Read more

    A Class Representative Model for Pure Parsimony Haplotyping

  • Daniele Catanzaro
  • Martine Labbé
  • Alessandra Godi
    • Categories (Mixed) Integer Linear Programming, Basic Sciences Applications Tags , ,

    Parsimonious haplotype estimation from aligned Single Nucleotide Polymorphism (SNP) fragments consists of finding the minimum number of haplotypes necessary to explain a given set of genotypes. This problem is known to be NP-Hard. Here we describe a new integer linear-programming model to tackle this problem based on the concept of class representatives, already used for … Read more

    Dissimilarity Measures for Population-Based Global Optimization Algorithms

  • Andrea Cassioli
  • Marco Locatelli
  • Fabio Schoen
    • Categories Basic Sciences Applications, Global Optimization, Stochastic Approaches Tags , , ,

    Very hard optimization problems, i.e., problems with a large number of variables and local minima, have been effectively attacked with algorithms which mix local searches with heuristic procedures in order to widely explore the search space. A Population Based Approach based on a Monotonic Basin Hopping optimization algorithm has turned out to be very effective … Read more

    A General Heuristic Method for Joint Chance-Constrained Stochastic Programs with Discretely Distributed Parameters

  • Eric B. Beier
  • Matthew W. Tanner
    • Categories Basic Sciences Applications, Meta Heuristics, Stochastic Programming Tags , , ,

    We present a general metaheuristic for joint chance-constrained stochastic programs with discretely distributed parameters. We give a reformulation of the problem that allows us to define a finite solution space. We then formulate a novel neighborhood for the problem and give methods for efficiently searching this neighborhood for solutions that are likely to be improving. … Read more

    Continuous Optimization Methods for Structure Alignments

  • Roberto Andreani
  • Leandro Martínez
  • José Mario Martínez
  • Flavio Yano
    • Categories Basic Sciences Applications, Nonlinear Optimization Tags , , , ,

    Structural Alignment is an important tool for fold identification of proteins, structural screening on ligand databases, pharmacophore identification and other applications. In the general case, the optimization problem of superimposing two structures is nonsmooth and nonconvex, so that most popular methods are heuristic and do not employ derivative information. Usually, these methods do not admit … Read more

    Solving a Quantum Chemistry problem with Deterministic Global Optimization

  • Marco Antonio Chaer Nascimento
  • Carlile Lavor
  • Leo Liberti
  • Nelson Maculan
    • Categories Basic Sciences Applications, Biomedical Applications, Global Optimization Applications Tags , , ,

    The Hartree-Fock method is well known in quantum chemistry, and widely used to obtain atomic and molecular eletronic wave functions, based on the minimization of a functional of the energy. This gives rise to a multi-extremal, nonconvex, polynomial optimization problem. We give a novel mathematical programming formulation of the problem, which we solve by using … Read more

    Density-based Globally Convergent Trust-Region Methods for Self-Consistent Field Electronic Structure Calculations

  • Juliano B. Francisco
  • Leandro Martínez
  • José Mario Martínez
    • Categories Basic Sciences Applications, Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , ,

    A theory of globally convergent trust-region methods for self-consistent field electronic structure calculations that use the density matrices as variables is developed. The optimization is performed by means of sequential global minimizations of a quadratic model of the true energy. The global minimization of this quadratic model, subject to the idempotency of the density matrix … Read more