Draft of Paper Appearing In: %a L. Ingber %t Very Fast Simulated Re-annealing %j Mathl. Comput. Modelling %v 12 Very Fast Simulated Re-annealing Very Fast Re-annealing -2- Lester Ingber

An algorithm is developed to statistically find the best global fit of a nonlinear non-convex cost-function over a D-dimensional space. It is argued that this algorithm permits an annealing schedule for ''temperature'' T decreasing exponentially in annealing-time k, T = T 0 exp(−ck 1/D). The introduction of re-annealing also permits adaptation to changing sensitivities in the multi-dimensional parameter-space. This annealing schedule is faster than fast Cauchy annealing, where T = T 0 /k, and much faster than Boltzmann annealing, where T = T 0 / ln k. Applications are being made to fit empirical data to Lagrangians representing nonlinear Gaussian-Markovian systems. I. Introduction Modeling phenomena is as much a cornerstone of 20th century Science as is collection of empirical data [1]. Modeling is essential to go beyond current knowledge, to better understand new or complex phenomena. Many instances arise in essentially all fields of Science when mathematical models of the real world become tested by fitting some parameters to empirical data. Since the real world is often nonlinear and stochastic, it is not surprising that often this process involves fitting statistical, nonlinear, non-convex functional forms to data. Physical methods of ''simulated annealing'' hav e been found to be extremely useful tools for this purpose in a wide variety of examples. This paper contributes to this methodology by presenting an improvement over previous algorithms. Sections II and III give a short outline of previous Boltzmann annealing (BA) and fast Cauchy fast annealing (FA) algorithms. Section IV presents the new very fast algorithm. Section V enhances this algorithm with a re-annealing modification found to be extremely useful for multi-dimensional parameter-spaces. This method will be referred to here as very fast re-annealing (VFR). Section VI gives an outline of some applications presently using this new algorithm. Section VII gives a short discussion.