2,136 research outputs found
Structural Optimization Using the Newton Modified Barrier Method
The Newton Modified Barrier Method (NMBM) is applied to structural optimization problems with large a number of design variables and constraints. This nonlinear mathematical programming algorithm was based on the Modified Barrier Function (MBF) theory and the Newton method for unconstrained optimization. The distinctive feature of the NMBM method is the rate of convergence that is due to the fact that the design remains in the Newton area after each Lagrange multiplier update. This convergence characteristic is illustrated by application to structural problems with a varying number of design variables and constraints. The results are compared with those obtained by optimality criteria (OC) methods and by the ASTROS program
On representations of the feasible set in convex optimization
We consider the convex optimization problem where is convex, the feasible set K is convex and Slater's
condition holds, but the functions are not necessarily convex. We show
that for any representation of K that satisfies a mild nondegeneracy
assumption, every minimizer is a Karush-Kuhn-Tucker (KKT) point and conversely
every KKT point is a minimizer. That is, the KKT optimality conditions are
necessary and sufficient as in convex programming where one assumes that the
are convex. So in convex optimization, and as far as one is concerned
with KKT points, what really matters is the geometry of K and not so much its
representation.Comment: to appear in Optimization Letter
Molecular second-quantized Hamiltonian:Electron correlation and non-adiabatic coupling treated on an equal footing
We introduce a new theoretical and computational framework for treating molecular quantum mechanics without the Born–Oppenheimer approximation. The molecular wavefunction is represented in a tensor-product space of electronic and vibrational basis functions, with electronic basis chosen to reproduce the mean-field electronic structure at all geometries. We show how to transform the Hamiltonian to a fully second-quantized form with creation/annihilation operators for electronic and vibrational quantum particles, paving the way for polynomial-scaling approximations to the tensor-product space formalism. In addition, we make a proof-of-principle application of the new Ansatz to the vibronic spectrum of C2
Ultrafast Photoinduced Dynamics of 1,3-Cyclohexadiene Using XMS-CASPT2 Surface Hopping
A full-dimensional simulation of the photodissociation of 1,3-cyclohexadiene in the manifold of three electronic states was performed via nonadiabatic surface hopping dynamics using extended multistate complete active space second-order perturbation (XMS-CASPT2) electronic structure theory with fully analytic nonadiabatic couplings. With the 47 ± 8% product quantum yield calculated from the 136 trajectories, generally 400 fs-long, and an estimated excited lifetime of 89 ± 9 fs, our calculations provide a detailed description of the nonadiabatic deactivation mechanism, showing the existence of an extended conical intersection seam along the reaction coordinate. The nature of the preferred reaction pathways on the ground state is discussed and extensive comparison to the previously published full dimensional dynamics calculations is provided
Fast Primal-Dual Gradient Method for Strongly Convex Minimization Problems with Linear Constraints
In this paper we consider a class of optimization problems with a strongly
convex objective function and the feasible set given by an intersection of a
simple convex set with a set given by a number of linear equality and
inequality constraints. A number of optimization problems in applications can
be stated in this form, examples being the entropy-linear programming, the
ridge regression, the elastic net, the regularized optimal transport, etc. We
extend the Fast Gradient Method applied to the dual problem in order to make it
primal-dual so that it allows not only to solve the dual problem, but also to
construct nearly optimal and nearly feasible solution of the primal problem. We
also prove a theorem about the convergence rate for the proposed algorithm in
terms of the objective function and the linear constraints infeasibility.Comment: Submitted for DOOR 201
Sums over Graphs and Integration over Discrete Groupoids
We show that sums over graphs such as appear in the theory of Feynman
diagrams can be seen as integrals over discrete groupoids. From this point of
view, basic combinatorial formulas of the theory of Feynman diagrams can be
interpreted as pull-back or push-forward formulas for integrals over suitable
groupoids.Comment: 27 pages, 4 eps figures; LaTeX2e; uses Xy-Pic. Some ambiguities
fixed, and several proofs simplifie
Global stabilization of fixed points using predictive control
We analyze the global stability properties of some methods of predictive control. We particularly focus on the optimal control function introduced by de Sousa Vieira and Lichtenberg [Phys. Rev. E54, 1200 (1996)]. We rigorously prove that it is possible to use this method for the global stabilization of a discrete system xn+1=f(xn) into a positive equilibrium for a class of maps commonly used in population dynamics. Moreover, the controlledsystem is globally stable for all values of the control parameter for which it is locally asymptotically stable. Our study highlights the difficulty of obtaining global stability results for other methods of predictive control, where higher iterations of f are used in the control scheme.Ministerio de Ciencia e InnovaciónFondo Europeo de Desarrollo Regiona
Self-association of the Shigella flexneri IcsA autotransporter protein
The IcsA autotransporter protein is a major virulence factor of the human intracellular pathogen Shigella flexneri. IcsA is distributed at the poles in the outer membrane (OM) of S. flexneri and interacts with components of the host actin-polymerization machinery to facilitate intracellular actin-based motility and subsequent cell-to-cell spreading of the bacterium. We sought to characterize the biochemical properties of IcsA in the bacterial OM. Chemical cross-linking data suggested that IcsA exists in a complex in the OM. Furthermore, reciprocal co-immunoprecipitation of differentially epitope-tagged IcsA proteins indicated that IcsA is able to self-associate. The identification of IcsA linker-insertion mutants that were negatively dominant provided genetic evidence of IcsA–IcsA interactions. From these results, we propose a model whereby IcsA self-association facilitates efficient actin-based motility.Kerrie L. May, Marcin Grabowicz, Steven W. Polyak and Renato Moron
Molecular-orbital-free algorithm for excited states in time-dependent perturbation theory
A non-linear conjugate gradient optimization scheme is used to obtain
excitation energies within the Random Phase Approximation (RPA). The solutions
to the RPA eigenvalue equation are located through a variational
characterization using a modified Thouless functional, which is based upon an
asymmetric Rayleigh quotient, in an orthogonalized atomic orbital
representation. In this way, the computational bottleneck of calculating
molecular orbitals is avoided. The variational space is reduced to the
physically-relevant transitions by projections. The feasibility of an RPA
implementation scaling linearly with system size, N, is investigated by
monitoring convergence behavior with respect to the quality of initial guess
and sensitivity to noise under thresholding, both for well- and ill-conditioned
problems. The molecular- orbital-free algorithm is found to be robust and
computationally efficient providing a first step toward a large-scale, reduced
complexity calculation of time-dependent optical properties and linear
response. The algorithm is extensible to other forms of time-dependent
perturbation theory including, but not limited to, time-dependent Density
Functional theory.Comment: 9 pages, 7 figure
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