No abstract

Zero-norm, Concave optimization, Frank-Wolfe algorithm, Feature selection,

The Morse potential is a simple model pair potential that has a single parameter ρ which determines the width of the potential well and allows a wide variety of materials to be modelled. Morse clusters provide a particularly tough test system for global optimization algorithms, and one that is highly relevant to methods that are to be applied to find the optimal configuration of a biomolecule. In particular, large ρ values are very challenging and, until now, no unbiased global optimization method has been able to detect all the (putative) global minima at ρ = 14 for clusters with up to N = 80 atoms. In this paper we introduce some techniques for transforming the original Morse potential that allow us to considerably increase the efficiency in locating the known global minima and also to discover some new optimal clusters. These methods are promising candidates for application to the optimization of biomolecules. (Morse potential; global optimization; basin-hopping; two-phase local search)

In this paper stochastic algorithms for global optimization are reviewed. After a brief introduction on random-search techniques, a more detailed analysis is carried out on the application of simulated annealing to continuous global optimization. The aim of such an analysis is mainly that of presenting recent papers on the subject, which have received only scarce attention in the most recent published surveys. Finally a very brief presentation of clustering techniques is given.

Global optimization, Space trajectories, Implicit filter, Black-box, Basin hopping,