Past

In many applications of interest, such as the conformational

dynamics of molecules, large deterministic systems can exhibit

stochastic behaviour in a relative small number of coarse-grained

variables. This kind of dimension reduction, from a large deterministic

system to a smaller stochastic one, can be very useful in understanding

the problem. Whilst the subject of statistical mechanics provides

a wealth of explicit examples where stochastic models for coarse

variables can be found analytically, it is frequently the case

that applications of interest are not amenable to analytic

dimension reduction. It is hence of interest to pursue computational

algorithms for such dimension reduction. This talk will be devoted

to describing recent work on parameter estimation aimed at

problems arising in this context.

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Joint work with Raz Kupferman (Jerusalem) and Petter Wiberg (Warwick)

A new filter method will be presented that attempts to find a feasible

point for sets of nonlinear sets of equalities and inequalities. The

method is intended to work for problems where the number of variables

or the number of (in)equalities is large, or both. No assumption is

made about convexity. The technique used is that of maintaining a list

of multidimensional "filter entries", a recent development of ideas

introduced by Fletcher and Leyffer. The method will be described, as

well as large scale numerical experiments with the corresponding

Fortran 90 module, FILTRANE.