Basic Sciences Applications – Page 8

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

Published: 2007/08/21, Updated: 2008/05/24

Basic Sciences Applications, Meta Heuristics, Stochastic Programming optimization, stochastic programming, tabu search, vaccine allocation

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

Published: 2006/01/30, Updated: 2006/06/02

Basic Sciences Applications, Nonlinear Optimization continuous optimization, gauss-newton method, order-value optimization, protein alignment, structural alignment

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

Published: 2005/07/12

Basic Sciences Applications, Biomedical Applications, Global Optimization Applications Branch-and-Bound, global optimization, hartree-fock method, reduction constraints

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

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

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

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

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