Vinkó, Tamás

Vinkó Tamás

University of Szeged

Reliable global optimization on atom clustersTamás VinkóGiven a cluster of  atoms define    	  	        as the center of the 	th atom. Thepotential energy function of the cluster             	 is defined by the summation ofthe two-body inter-particle pair potentials over all of the pairs, i.e.7        	        where  is the Euclidean distance and        is the pair-potential function. The globaloptimization of a potential energy function describing an atom cluster is a challenge for thescientific computing. Recently many papers deal with this problem, especially the so calledLennard-Jones problem, where the pair-potential function is defined as    where  is the atom-pair distance. However, one can find no paper about reliable method forfinding the optimal structure of Lennard-Jones atom clusters. Branch-and-bound type methodsbased on interval arithmetic could produce reliable solution for global optimization problems.In this talk the Lennard-Jones atom cluster problem will be considered with the reliable pointof view. First, we establish good lower bound for the minimal inter-atomic distance in theoptimal structure (independently from the number of atoms). From this result a guaranteedlower bound for the global optimum will be given which is a linear function of the numberof atoms. Using this results and geometrical considerations we will introduce an optimizationmethod producing guaranteed globally optimal solutions.126

Reliable global optimization on atom clusters : [abstract]

http://acta.bibl.u-szeged.hu/59820/1/cscs_2004_126.pdf

Reliable global optimization on atom clusters

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