Incremental Gradient Algorithms with Stepsizes Bounded Away from Zero

We consider the class of incremental gradient methods for minimizing a sum of continuously differentiable functions. An important novel feature of our analysis is that the stepsizes are kept bounded away from zero. We derive the first convergence results of any kind for this computationally important case. In particular, we show that a certain -approximate solution can be obtained and establish the linear dependence of on the stepsize limit. Incremental gradient methods are particularly well-suited for large neural network training problems where obtaining an approximate solution is typically sufficient and is often preferable to computing an exact solution. Thus, in the context of neural networks, the approach presented here is related to the principle of tolerant training. Our results justify numerous stepsize rules that were derived on the basis of extensive numerical experimentation but for which no theoretical analysis was previously available. In addition, convergence to (exact) stationary points is established when the gradient satisfies a certain growth property.     

Error bounds for 2-regular mappings with Lipschitzian derivatives and their applications

We obtain local estimates of the distance to a set defined by equality constraints under assumptions which are weaker than those previously used in the literature. Specifically, we assume that the constraints mapping has a Lipschitzian derivative, and satisfies a certain 2-regularity condition at the point under consideration. This setting directly subsumes the classical regular case and the twice differentiable 2-regular case, for which error bounds are known, but it is significantly richer than either of these two cases. When applied to a certain equation-based reformulation of the nonlinear complementarity problem, our results yield an error bound under an assumption more general than b-regularity. The latter appears to be the weakest assumption under which a local error bound for complementarity problems was previously available. We also discuss an application of our results to the convergence rate analysis of the exterior penalty method for solving irregular problems. Received: February 2000 / Accepted: November 2000?Published online January 17, 2001     

Wärmeübergang bei einphasiger freier Konvektion in der Nähe des kritischen Zustandes

Zusammenfassung Mit den Halogenkältemitteln R12 (CF₂Cl₂), R115 (C₂F₅Cl) und RC318 (C₄F_S) wurden an einem elektrisch beheizten, horizontalen Rohr (d=8 mm) Versuche zur einphasigen freien Konvektion in der Nähe des kritischen Zustandes durchgeführt. Die Messungen erstrecken sich von etwa der halben bis zur doppelten kritischen Dichte und zum 1,8-fachen kritischen Druck; dabei wurden die Fluidzustände außerhalb der beheizten Zone längs der kritischen und einer überkritischen Isotherme variiert.Je nach dem Ausgangszustand des Fluids ist die Abhängigkeit des Wärmeübergangskoeffizienten von der Heizflächenbelastung q ähnlich wie beim Filmsieden oder wie bei freier Konvektion weit unterkritischer Fluide, oder es treten Maxima im (q)-Zusammenhang auf. Die unterschiedlichen Ergebnisse können durch Analyse des Dichte- bzw. Enthalpieverlaufs in der wandnahen, beheizten Fluidzone erklärt werden.

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Free convective heat transfer near the critical state

Experiments were performed on free convective heat transfer from a horizontal, electrically heated tube (d=8 mm) to the halocarbon refrigerants R12 (CF₂Cl₂), R115 (C₂F₅Cl) and RC318 (C₄F₈) near the critical state. Density varied from approx. half to twice the critical value and pressure up to 1.8 times the critical value; the bulk fluid state was varied along the critical and one supercritical isotherm.As is partially known, at different bulk fluid states either peaks are found in the heat transfer coefficients as a function of heat flux or a behaviour similar to film boiling or to free convection at far subcritical states is observed. The different results can be explained by analyzing the density- and enthalpy-variation within the fluid near the heated wall.

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Herrn Prof. Dr.-Ing. H. Glaser, Stuttgart, zum 70. Geburtstag gewidmet.

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Die für die vorliegende Arbeit verwendete versuschanlage wurde mit Mitteln aus dem Schwepunktprogramm Siedevorgänge der Deutschen Forschungsgemeinschaft aufgebaut. Die als Versuchsstoffe benutzten Kältemittel wurden dankenswerterweise von don Farbwerken Hoechst zur Verfügung gestellt.     

Scaling hot-electron generation to high-power, kilojoule-class laser-solid interactions

Thin-foil targets were irradiated with high-power (1 ≤ P(L) ≤ 210 TW), 10-ps pulses focused to intensities of I>10(18) W/cm(2) and studied with K-photon spectroscopy. Comparing the energy emitted in K photons to target-heating calculations shows a laser-energy-coupling efficiency to hot electrons of η(L-e) = 20 ± 10%. Time-resolved x-ray emission measurements suggest that laser energy is coupled to hot electrons over the entire duration of the incident laser drive. Comparison of the K-photon emission data to previous data at similar laser intensities shows that η(L-e) is independent of laser-pulse duration from 1 ≤ τ(p) ≤ 10 ps.     

Parallel Variable Distribution for Constrained Optimization

In the parallel variable distribution framework for solving optimization problems (PVD), the variables are distributed among parallel processors with each processor having the primary responsibility for updating its block of variables while allowing the remaining secondary variables to change in a restricted fashion along some easily computable directions. For constrained nonlinear programs convergence theory for PVD algorithms was previously available only for the case of convex feasible set. Additionally, one either had to assume that constraints are block-separable, or to use exact projected gradient directions for the change of secondary variables. In this paper, we propose two new variants of PVD for the constrained case. Without assuming convexity of constraints, but assuming block-separable structure, we show that PVD subproblems can be solved inexactly by solving their quadratic programming approximations. This extends PVD to nonconvex (separable) feasible sets, and provides a constructive practical way of solving the parallel subproblems. For inseparable constraints, but assuming convexity, we develop a PVD method based on suitable approximate projected gradient directions. The approximation criterion is based on a certain error bound result, and it is readily implementable. Using such approximate directions may be especially useful when the projection operation is computationally expensive.     

A generalization of the denjoy integral

We prove that the IsekiM-integral is substantially more general than the Denjoy integral. Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 766–772, November, 1997. Translated by I. P. Zvyagin     

Pentaerythritol-based demulsifying agents and their surfactant properties

Pentaerythritol-based block copolymers of ethylene and propylene oxides were synthesized and characterized as surfactants and demulsifiers.     

Measurement of the negative muon anomalous magnetic moment to 0.7 ppm

The anomalous magnetic moment of the negative muon has been measured to a precision of 0.7 ppm (ppm) at the Brookhaven Alternating Gradient Synchrotron. This result is based on data collected in 2001, and is over an order of magnitude more precise than the previous measurement for the negative muon. The result a(mu(-))=11 659 214(8)(3) x 10(-10) (0.7 ppm), where the first uncertainty is statistical and the second is systematic, is consistent with previous measurements of the anomaly for the positive and the negative muon. The average of the measurements of the muon anomaly is a(mu)(exp)=11 659 208(6) x 10(-10) (0.5 ppm).     

Absorption spectrum of H<Stack><Subscript>3</Subscript><Superscript>+</Superscript></Stack> near 1.06 μm

The absorption spectra of molecular hydrogen plasma excited by electric hollow-cathode and high-frequency discharges are measured. The spectra in the region of 1.06 μm were recorded using a neodymium intracavity laser spectrometer with a resolution of 0.03 cm^?1 and an absorption sensitivity of 10^?8 cm^?1. The absorption lines that can be attributed to the transitions to vibrational states in the molecule are recorded.