Basic Sciences Applications

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

    An Explicit Semidefinite Characterization of Satisfiability for Tseitin Instances

  • Miguel F. Anjos
    • Categories 0-1 Programming, Basic Sciences Applications, Semi-definite Programming Tags , , , ,

    This paper is concerned with the application of semidefinite programming to the satisfiability problem, and in particular with using semidefinite liftings to efficiently obtain proofs of unsatisfiability. We focus on the Tseitin satisfiability instances which are known to be hard for many proof systems. We present an explicit semidefinite programming problem with dimension linear in … Read more

    Large-scale semidefinite programs in electronic structure calculation

  • Bastiaan J. Braams
  • Mituhiro Fukuda
  • Michael L. Overton
  • Maho Nakata
  • Jerome K. Percus
  • Makoto Yamashita
  • Zhengji Zhao
    • Categories Basic Sciences Applications, Semi-definite Programming Tags , , , , ,

    Employing the variational approach having the two-body reduced density matrix (RDM) as variables to compute the ground state energies of atomic-molecular systems has been a long time dream in electronic structure theory in chemical physics/physical chemistry. Realization of the RDM approach has benefited greatly from recent developments in semidefinite programming (SDP). We present the actual … Read more

    On the control of an evolutionary equilibrium in micromagnetics

  • Michal Kočvara
  • Martin Kružík
  • Jiri V. Outrata
    • Categories Basic Sciences Applications, Complementarity and Variational Inequalities, Systems governed by Differential Equations Optimization Tags , , , ,

    We formulate an optimal control problem of magnetization in a ferromagnet as a mathematical program with evolutionary equilibrium constraints. The evolutionary nature of the equilibrium is due to the hysteresis behavior of the respective magnetization process. To solve the problem numerically, we adapted the implicit programming technique. The adjoint equations, needed to compute the subgradients … 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

    Second-order Cone Programming Methods for Total Variation-based Image Restoration

  • Donald Goldfarb
  • Wotao Yin
    • Categories Basic Sciences Applications, Second-Order Cone Programming Tags , , , , ,

    In this paper we present optimization algorithms for image restoration based on the total variation (TV) minimization framework of L. Rudin, S. Osher and E. Fatemi (ROF). Our approach formulates TV minimization as a second-order cone program which is then solved by interior-point algorithms that are efficient both in practice (using nested dissection and domain … Read more

    The Reduced Density Matrix Method for Electronic Structure Calculations and the Role of Three-Index Representability Conditions

  • Bastiaan J. Braams
  • Mituhiro Fukuda
  • Michael L. Overton
  • Jerome K. Percus
  • Zhengji Zhao
    • Categories Basic Sciences Applications, Convex Optimization, Semi-definite Programming Tags

    The variational approach for electronic structure based on the two-body reduced density matrix is studied, incorporating two representability conditions beyond the previously used $P$, $Q$ and $G$ conditions. The additional conditions (called $T1$ and $T2$ here) are implicit in work of R.~M.~Erdahl [Int.\ J.\ Quantum Chem.\ {\bf13}, 697–718 (1978)] and extend the well-known three-index diagonal … Read more

    The global optimization of Morse clusters by potential energy transformations

  • Jon P. K. Doye
  • Marco Locatelli
  • Robert H. Leary
  • Fabio Schoen
    • Categories Basic Sciences Applications, Biomedical Applications, Stochastic Approaches

    The Morse potential is a simple model pair potential that has a single parameter $\rho$ which determines the width of the potential well and allows a wide variety of materials to be modelled. Morse clusters provide a particularly tough test system for global optimization algorithms, and one that is highly relevant to methods that are … Read more

    New global optima for Morse clusters at $\rho=8$

  • Marco Locatelli
  • Fabio Schoen
    • Categories Basic Sciences Applications, Stochastic Approaches Tags , ,

    We recently discovered 5 new putative globally optimum configurations for Morse clusters at $\rho=8$. This report contains some algorithmic details as well as the structures determined with our method. CitationTechnical Report DSI 3-2003, Dipartimento di Sistemi e Informatica, Università degli Studi di Firenze, Firenze, 2003.ArticleDownload View PDF

    The Thirteen Spheres: A New Proof

  • Kurt M. Anstreicher
    • Categories Basic Sciences Applications Tags , , ,

    The “thirteen spheres problem”, also known as the “Gregory-Newton problem” is to determine the maximum number of three-dimensional spheres that can simultaneously touch a given sphere, where all the spheres have the same radius. The history of the problem goes back to a disagreement between Isaac Newton and David Gregory in 1694. Using a combination … Read more