New Bundle Methods for Solving Lagrangian Relaxation Dual Problems

Bundle methods have been used frequently to solve nonsmooth optimization problems. In these methods, subgradient directions from past iterations are accumulated in a bundle, and a trial direction is obtained by performing quadratic programming based on the information contained in the bundle. A line search is then performed along the trial direction, generating a serious step if the function value is improved by or a null step otherwise. Bundle methods have been used to maximize the nonsmooth dual function in Lagrangian relaxation for integer optimization problems, where the subgradients are obtained by minimizing the performance index of the relaxed problem. This paper improves bundle methods by making good use of near-minimum solutions that are obtained while solving the relaxed problem. The bundle information is thus enriched, leading to better search directions and less number of null steps. Furthermore, a simplified bundle method is developed, where a fuzzy rule is used to combine linearly directions from near-minimum solutions, replacing quadratic programming and line search. When the simplified bundle method is specialized to an important class of problems where the relaxed problem can be solved by using dynamic programming, fuzzy dynamic programming is developed to obtain efficiently near-optimal solutions and their weights for the linear combination. This method is then applied to job shop scheduling problems, leading to better performance than previously reported in the literature.     

VARIATIONAL PROPERTIES OF THE INTEGRATED MEAN CURVATURES OF TUBES IN SYMMETRIC SPACES

61. IntroductionLet P be a submanifold of an n-dimensional riemannian manifold AI. Expressions fOrthe kth integrated mean curvatures, M^P(t), (i. e. the integral of tho kth mcan curvature,k = 0, 1,' l n -- l), of a tubular hypersurface P of radius t about P, in terms of theRiemann curvature tensor of P. are calculated when AI is Euclidean or a rank one symmetricspace[5'13"1. Moreover, when P is a closed convex hypersurface of thc n-dimensional spaceof constant curvature A', Santal6 has…     

Near Best Tree Approximation

Tree approximation is a form of nonlinear wavelet approximation that appears naturally in applications such as image compression and entropy encoding. The distinction between tree approximation and the more familiar n-term wavelet approximation is that the wavelets appearing in the approximant are required to align themselves in a certain connected tree structure. This makes their positions easy to encode. Previous work [4,6] has established upper bounds for the error of tree approximation for certain (Besov) classes of functions. This paper, in contrast, studies tree approximation of individual functions with the aim of characterizing those functions with a prescribed approximation error. We accomplish this in the case that the approximation error is measured in L ₂, or in the case p2, in the Besov spaces B _p ⁰(L _p ), which are close to (but not the same as) L _p . Our characterization of functions with a prescribed approximation order in these cases is given in terms of a certain maximal function applied to the wavelet coefficients.     

A BODY MASS DEPENDENT MECHANICAL IMPEDANCE MODEL FOR APPLICATIONS IN VIBRATION SEAT TESTING

A three degree-of-freedom model is proposed to predict the biodynamic responses of the seated human body of different masses. A baseline model is initially derived to satisfy both the mean apparent mass and seat-to-head transmissibility responses proposed in ISO/DIS 5982:2000 applicable for mean body mass of 75 kg. The validity of the resultant generic mass dependent model is verified by comparing the apparent mass and driving-point mechanical impedance responses computed for total body masses of 55, 75 and 90 kg with the range of idealized values proposed for body masses within the 49-93 kg range. Considering the lack of data that could be found to define the apparent mass/mechanical impedance of subjects with different body masses when applying the experimental conditions defined in ISO/DIS 5982:2000, an attempt is made to adapt the parameters of the base model to fit the measured apparent mass data applicable to groups of automobile occupants within different mass ranges. This is achieved through constrained parametric optimization which consists of minimizing the sum of squared errors between the computed response and the mean apparent mass data measured for automobile occupants within four mass groups: less than 60 kg, 60·5-70·5 kg, 70·5-80 kg and above 80 kg. The results show a reasonably good agreement between the model responses and the measured apparent mass data, particularly at frequencies below 10 Hz. The results suggest that the proposed mass dependent model can effectively predict the apparent mass responses of automobile occupants over a wide range of body masses and for two different postures: passenger (hands-in-lap) and driver (hands-on-steering wheel) postures.     

Spectrophotometric determination of phenylephrine hydrochloride in pharmaceuticals by flow injection analysis exploiting the reaction with potassium ferricyanide and 4-aminoantipyrine

This paper presents a method for the determination of phenylephrine hydrochloride in pharmaceuticals by spectrophotometric flow injection analysis exploiting the reaction with potassium ferricyanide and 4-aminoantipyrine, which leads to the formation of a condensation product with strong absorptivity at 500 nm. The linear dynamic range was between 0.95 and 9 mg/L, with a limit of detection of 0.2 mg/L and a sampling throughput of 120 samples per hour. The method was applied to eyewashes and nasal decongestant liquid medicines.     

Novel sb induced reconstruction of the (113) surface of ge

Sb induces on Ge(113) a c(2 x 2) reconstruction in which Sb breaks one Ge-Ge bond and occupies an interstitial site, in contrast to Sb adsorption on other Si or Ge surfaces. Sb saturates the three dangling bonds per unit cell of the (113) surface inducing a large strain which is released by occupation of the interstitial site. Two neighboring Sb at interstitial sites form a dimer. The structure has been determined by x-ray diffraction, applying direct methods, and ab initio density-functional-theory calculations. The adsorption geometry and the high binding energy lead one to expect that Sb cannot be used as a surfactant for the growth of Si/Ge layers on the (113) surface.     

Experimental and numerical studies of noise-induced coherent patterns in a subexcitable system

A subexcitable medium of Belousov-Zhabotinsky (BZ) reaction subjected to external Gaussian white noise is studied in experiments and numerical simulations. We observe that at an optimal level of noise the wave sources of excited traveling waves become synchronous, as though there exists a long distance spatial correlation. The synchronous behavior fades if the noise level becomes larger or smaller. Numerical simulations confirm the experimental findings, and point out that the best synchronous behavior takes place when the signal-to-noise ratio of waves becomes largest.     

Discharges in the JET tokamak where the safety factor profile is identified as the critical factor for triggering internal transport barriers

Joint European Torus discharges which demonstrate the critical role the safety factor profile, q, can play in the formation of internal transport barriers (ITB) are examined. In these discharges, the target parameters, including the E x B flows, were kept virtually the same, except for the q profile. In a discharge with a nonmonotonic q, an ITB was triggered whereas a discharge with monotone q made no such transition. Thus, there is strong evidence that the q profile was the critical factor for the triggering of an ITB. Possible interpretations of this finding are discussed.     

Observation of unusual surface ordering in a uniaxial Sm-A phase formed by a highly biaxial compound

We have studied one banana-shaped compound using null-transmission ellipsometry. By studying free-standing films of various thicknesses we confirm that this compound exhibits the Sm-A phase. This is the first banana-shaped compound with a relatively small bend angle (approximately 140 degrees) in which a uniaxial phase has been observed. At the lower temperature end of the Sm-A phase we observe unusual ordering at the surface of the film.