We i n troduce the basic notions of Automatic Di erentiation, describe some extensions which are of interest in the context of nonlinear optimization and give some illustrative examples.

ABSTRACT.We have built and used on several occasions an optical broadband stellar polarimeter, PlanetPol, which employs photoelastic modulators and avalanche photodiodes and achieves a photon-noise-limited sensitivity of at least 1 in 10 6 in fractional polarization. Observations of a number of polarized standards taken from the literature show that the accuracy of polarization measurements is ∼1%. We have developed a method for accurately measuring the polarization of altitude-azimuth mounted telescopes by observing bright nearby stars at different parallactic angles, and we find that the on-axis polarization of the William Herschel Telescope is typically ∼15 # 10 Ϫ6 , measured with an accuracy of a few parts in 10 7 . The nearby stars (distance less than 32 pc) are found to have very low polarizations, typically a few #10 Ϫ6 , indicating that very little interstellar polarization is produced close to the Sun and that their intrinsic polarization is also low. Although the polarimeter can be used for a wide range of astronomy, the very high sensitivity was set by the goal of detecting the polarization signature of unresolved extrasolar planets.

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Aims and ScopeOptimization has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time, one of the most striking trends in optimization is the constantly increasing emphasis on the interdisciplinary nature of the field. Optimization has been a basic tool in all areas of applied mathematics, engineering, medicine, economics and other sciences.The Springer Series in Optimization and Its Applications publishes undergraduate and graduate textbooks, monographs and state-of-the-art expository works that focus on algorithms for solving optimization problems and also study applications involving such problems. Some of the topics covered include nonlinear optimization (convex and nonconvex), network flow problems, stochastic optimization, optimal control, discrete optimization, multiobjective programming, description of software packages, approximation techniques and heuristic approaches.

Abstract. Numerical methods of solving the inverse light scattering problem for spheres are presented. The methods are based on two stochastic global optimization techniques: Deep's random search and the multilevel single-linkage clustering analysis due to Rinnooy Kan and Timmer. Computational examples show that the radius and the refractive index of spheres comparable with or larger than the wavelength of light can be recovered from multiangle scattering data. While the random search approach is faster, the clustering analysis is shown to be more reliable. A general discussion of the clustering method is also given.