Basic Sciences Applications – Page 8

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

Published: 2005/07/10, Updated: 2006/02/18

Basic Sciences Applications, Constrained Nonlinear Optimization, Nonlinear Optimization convergence analysis, density functional theory, hartree-fock, kohn-sham, levenberg-marquardt, trust-region methods

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

Published: 2005/05/28, Updated: 2007/08/06

Miguel F. Anjos

0-1 Programming, Basic Sciences Applications, Semi-definite Programming combinatorial optimization, discrete optimization, global optimization, satisfiability problem, semidefinite programming

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

Published: 2005/02/25

Basic Sciences Applications, Semi-definite Programming computational chemistry, large-scale optimization, n-representability, parallel computing, reduced density matrix, semidefinite programming

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

Published: 2005/02/22, Updated: 2005/03/02

Michal Kočvara

Martin Kružík

Jiri V. Outrata

Basic Sciences Applications, Complementarity and Variational Inequalities, Systems governed by Differential Equations Optimization coderivatives, ferromagnetism, hysteresis, implicit programming technique, mathematical programs with equilibrium constraints

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

Published: 2004/11/04

Antonis Argyros

Manolis Lourakis

Basic Sciences Applications, Nonlinear Systems and Least-Squares, Optimization Software and Modeling Systems 3d reconstruction, bundle adjustment, computer vision, levenberg-marquardt, non linear least squares, structure and motion estimation

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

Published: 2004/08/08

Donald Goldfarb

Wotao Yin

Basic Sciences Applications, Second-Order Cone Programming domain decomposition, image denoising, interior point methods, nested dissection, secon-order cone programming, total variation

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

Published: 2003/10/16

Basic Sciences Applications, Convex Optimization, Semi-definite Programming large scale semidefinite programming

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

Published: 2003/07/15, Updated: 2003/07/17

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 $\rho=8$

Published: 2003/03/14

Marco Locatelli

Fabio Schoen

Basic Sciences Applications, Stochastic Approaches global optimization, molecular conformation, morse clusters

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. Citation Technical Report DSI 3-2003, Dipartimento di Sistemi e Informatica, Università degli Studi di Firenze, Firenze, 2003. Article Download View New global optima for Morse clusters … Read more

The Thirteen Spheres: A New Proof

Published: 2002/10/28

Kurt M. Anstreicher

Basic Sciences Applications delaunay triangulation, kissing problem, spherical codes, voronoi decomposition

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