Pure adaptive search in monte carlo optimization

Pure adaptive search constructs a sequence of points uniformly distributed within a corresponding sequence of nested regions of the feasible space. At any stage, the next point in the sequence is chosen uniformly distributed over the region of feasible space containing all points that are equal or superior in value to the previous points in the sequence. We show that for convex programs the number of iterations required to achieve a given accuracy of solution increases at most linearly in the dimension of the problem. This compares to exponential growth in iterations required for pure random search.     

Optimality relationships forp-cyclic SOR

Summary The optimality question for blockp-cyclic SOR iterations discussed in Young and Varga is answered under natural conditions on the spectrum of the block Jacobi matrix. In particular, it is shown that repartitioning a blockp-cyclic matrix into a blockq-cyclic form,q, results in asymptotically faster SOR convergence for the same amount of work per iteration. As a consequence block 2-cyclic SOR is optimal under these conditions.Research supported in part by the US Air Force under Grant no. AFOSR-88-0285 and the National Science Foundation under grant no. DMS-85-21154 Present address: Boeing Computer Services, P.O. Box 24346, MS 7L-21, Seattle, WA 98124-0346, USA     

Transfer of near-infrared monochromator calibrations for tobacco constituents to tilting-filter instruments

Near-infrared calibrations for water, reducing sugar, glycerin, propylene glycol, nicotine, and menthol in tobacco blends were first obtained with a monochromator instrument. Transfer of calibrations to a tilting-filter instrument for factory trials is shown to be facilitated greatly by the computer-assisted scheme MTRAN. By means of this software, calibration equations were established for a Neotec 51A instrument that is sufficiently rugged for factory use. The predictive capabilities of the transferred calibrations are similar to those of the research monochromator.     

The existence of smooth densities for the prediction filtering and smoothing problems

The qualitative behavior of buckled states of two different models of elastic beams is studied. It is assumed that random imperfections affect the governing nonlinear equations. It is shown that near the first critical value of the buckling load the stochastic bifurcation is described asymptotically by an algebraic equation whose coeffficients are Gaussian random variables. The corresponding asymptotic expansion for the displacement is to lowest order a Gaussian stochastic process.Work supported by NSF Grant No. DCR81-14726.Work supported by NSF Grant No. DMS87-01895.     

Limits of parallelism in explicit ODE methods

Numerical methods for ordinary initial value problems that do not depend on special properties of the system are usually found in the class of linear multistage multivalue methods, first formulated by J.C. Butcher. Among these the explicit methods are easiest to implement. For these reasons there has been considerable research activity devoted to generating methods of this class which utilize independent function evaluations that can be performed in parallel. Each such group of concurrent function evaluations can be regarded as a stage of the method. However, it turns out that parallelism affords only limited opportunity for reducing the computing time with such methods. This is most evident for the simple linear homogeneous constant-coefficient test problem, whose solution is essentially a matter of approximating the exponential by an algebraic function. For a given number of stages and a given number of saved values, parallelism offers a somewhat enlarged set of algebraic functions from which to choose. However, there is absolutely no benefit in having the degree of parallelism (number of processors) exceed the number of saved values of the method. Thus, in particular, parallel one-step methods offer no speedup over serial one-step methods for the standard linear test problem. Although the implication of this result for general nonlinear problems is unclear, there are indications that dramatic speedups are not possible in general. Also given are some results relevant to the construction of methods.Work supported in part by National Science Foundation grants DMS 89 11410 and DMS 90 15533 and by US Department of Energy grant DOE DEFG02-87ER25026. Work of the second author was completed while at the University of Illinois.     

Scheduling real-time and non-real-time traffic under nonstationary conditions

In this paper a statistical multiplexer that processes a mixture of real-time and non-real-time traffic is studied under bursts of traffic. Different scheduling algorithms are compared under conditions when one of the classes of traffic has a sudden increase in its arrival rate during a short period of time. The results show a difference in the way the scheduling disciplines studied behave under short overloads of traffic even though the scheduling algorithms had been set up to give similar performance under steady-state arrivals. The lifetime of real-time packets is shown to have a great effect on the way in which the performance of the scheduling algorithms compare.Robert Lackman is an IBM employee in the IBM Resident Study Program.     

Sewings of crumpled cubes revisited

This paper sets forth three mismatch properties, strictly ordered in strength, about sewings of crumpled n-cubes. The strongest is a sufficient but not a necessary condition for a sewing to yield Sn, and the weakest, a necessary but not sufficient one. We show that when both crumpled cubes satisfies the Disjoint Disks Property, then the weakest property implies the sewing yields Sn, and we also show that the intermediate property leads to the same conclusion when just one of the crumpled cubes possesses the Disjoint Disks Property. In addition, we develop examples that confirm sharpness of the relevant Disjoint Disks conditions.