Globally Convergent BFGS Method for Nonsmooth Convex Optimization1

We propose an implementable BFGS method for solving a nonsmooth convex optimization problem by converting the original objective function into a once continuously differentiable function by way of the Moreau–Yosida regularization. The proposed method makes use of approximate function and gradient values of the Moreau-Yosida regularization instead of the corresponding exact values. We prove the global convergence of the proposed method under the assumption of strong convexity of the objective function.     

On the truncated conjugate gradient method

In this paper, we consider the truncated conjugate gradient method for minimizing a convex quadratic function subject to a ball trust region constraint. It is shown that the reduction in the objective function by the solution obtained by the truncated CG method is at least half of the reduction by the global minimizer in the trust region. Received January 19, 1999 / Revised version received October 1, 1999?Published online November 30, 1999     

The influence of polymer molecular-weight distributions on pulsed field gradient nuclear magnetic resonance self-diffusion experiments

 The influence of polymer molecular-weight distributions on the outcome of pulsed field gradient (PFG) NMR self-diffusion experiments has been considered. The self-diffusion coefficient, D, of monodisperse poly(ethylene oxide) (PEO) polymers has been determined in order to accurately determine the scaling behavior of D both with molecular weight and concentration. In order to investigate the influence of polydispersity on the PFG NMR signal, a model system consisting of ten reasonably monodisperse PEO polymers was made, and the PFG NMR signal intensities were recorded at a low total concentration. The data were analyzed using both inverse Laplace transformation and nonlinear least-squares fitting to a prescribed distribution function of D. Finally, the molecular-weight distribution was obtained by use of the values of the scaling parameters. We also present some model calculations used to investigate the sensitivity of the degree of polydispersity on the NMR signal decays. Received: 27 May 1999 Accepted in revised form: 19 October 1999     

Chromatographic behaviour of low molar-mass polyesters in normal-phase high-performance liquid chromatography

Summary The normal-phase chromatographic retention behaviour of polyesters on bare silica and on a polymer-based polyamine (PA) column has been studied with a variely of binary mobile phases under isocratic conditions. The dependence of experimental retention data on the degree of polymerization (p) and on mobile phase composition (φ) was characterized by to an approach developed by Jandera et al. The bulky repeating unit and the relatively highly polar end groups of the polyesters both had a large influence on retention behaviour. The two effects in combination explain the molar-mass-independent retention observed experimentally at a particular mobile phase composition for all the mobile phase—stationary phase combinations investigated. These conditions were found to be independent of the type of end group. End group separation on a silica column improves when the polarity of the less polar solvent is increased. End group separation is better on the PA column because of a greater difference between the adsorption energy of the alcohol and acid end groups. Better prediction of retention data on the PA column was achieved by use of an approach which assumes two different types of adsorption site. Results enabled further understanding of retention behaviour in normalphase gradient polymer-elution chromatography (NPGPEC) and explained both the dependence of the order of elution onp and differences between the end-group selectivity of different systems.     

高效液相色谱中用于梯度洗脱的有机溶剂的纯度测试

在反相高效液相色谱中,空白梯度基线的漂移和杂质峰,可能由含水溶剂和有机溶剂中杂质所引起的。当含水溶剂通过预柱在线净化后,根据空白梯度色谱图可测试有机溶剂的纯度。按照此法,对国产不同等级的乙腈和甲醇进行了测试,指明这些试剂用于梯度洗脱的可能性。     

SOLVING TRUST REGION PROBLEM IN LARGE SCALEOPTIMIZATION

1.IntroductionLetHbeagivennxnsymmetricpositivesemidefinitematrixandcER".Inthispaperweconsiderthefollowingquadraticprogrammingwithasimplequadraticalconstraint1r--XTH. CTX=min2(1)s.tIlxlls5a,wheretheparameteraisprescribed.Thisproblemoccursfrequentlyintrustrationmethodforunconstrainedoptimization[11.Anumberofapproachesforsolving(1)havebeenproposedintheliterature[2,3,6,12--16].OnetechniqueistoapproximateaLagrangemultiplierAbyNewton'smethod.Theapproximationofthisparametermaybequitedelicate,ho…     

A Quasi-Newton Quadratic Penalty Method for Minimization Subject to Nonlinear Equality Constraints

We present a modified quadratic penalty function method for equality constrained optimization problems. The pivotal feature of our algorithm is that at every iterate we invoke a special change of variables to improve the ability of the algorithm to follow the constraint level sets. This change of variables gives rise to a suitable block diagonal approximation to the Hessian which is then used to construct a quasi-Newton method. We show that the complete algorithm is globally convergent. Preliminary computational results are reported.     

Entanglement in a system of two two-level atoms interacting with a single-mode field

We investigate the entanglement in a system of two coupling atoms interacting with a single-mode field by means of quantum information entropy theory. The quantum entanglement between the two atoms and the coherent field is discussed by using the quantum reduced entropy, and the entanglement between the two coupling atoms is also investigated by using the quantum relative entropy. In addition, the influences of the atomic dipole--dipole interaction intensity and the average photon number of the coherent field on the degree of the entanglement is examined. The results show that the evolution of the degree of entanglement between the two atoms and the field is just opposite to that of the degree of entanglement between the two atoms. And the properties of the quantum entanglement in the system rely on the atomic dipole--dipole interaction and the average photon number of the coherent field.     

基于脉冲电铸技术Ni-ZrO2纳米梯度功能材料的制备工艺

研究了在脉冲复合电铸过程中,当其它工艺参数一定时,镀液中纳米ZrO2颗粒含量、脉间、脉宽和阴极电流密度对复合电铸层中ZrO2复合量和沉积速率以及脉冲参数对复合电铸层表面形貌的影响,并对所制备复合电铸层的横截面进行了SEM观察和组成成分测定.结果表明,通过控制脉冲复合电铸过程中的工艺参数可以制备出由纳米颗粒复合量变化而导致其组织成分呈梯度分布的纳米功能梯度材料.     

Reduced‐order modelling of an adaptive mesh ocean model

A novel proper orthogonal decomposition (POD) model has been developed for use with an advanced unstructured mesh finite‐element ocean model, the Imperial College Ocean Model (ICOM, described in detail below), which includes many recent developments in ocean modelling and numerical analysis. The advantages of the POD model developed here over existing POD approaches are the ability:

• 1. To increase accuracy when representing geostrophic balance (the balance between the Coriolis terms and the pressure gradient). This is achieved through the use of two sets of geostrophic basis functions where each one is calculated by basis functions for velocities u and v.
• 2. To speed up the POD simulation. To achieve this a new numerical technique is introduced, whereby a time‐dependent matrix in the discretized equation is rapidly constructed from a series of time‐independent matrices. This development imparts considerable efficiency gains over the often‐used alternative of calculating each finite element over the computational domain at each time level.
• 3. To use dynamically adaptive meshes in the above POD model.

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