An Infeasible Point Method for Minimizing the Lennard-JonesPotential

Authors:
Mark S. Gockenbach;Anthony J. Kearsley;William W. Symes
Affiliations:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-0001;Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899;Department of Computational & Applied Mathematics, Rice University, Houston, Texas 77251-1892
Venue:
Computational Optimization and Applications
Year:
1997

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Abstract

Minimizing the Lennard-Jones potential, the most-studied modelproblem for molecular conformation, is an unconstrained globaloptimization problem with a large number of local minima. In thispaper, the problem is reformulated as an equality constrainednonlinear programming problem with only linear constraints. Thisformulation allows the solution to approached through infeasibleconfigurations, increasing the basin of attraction of the globalsolution. In this way the likelihood of finding a global minimizeris increased. An algorithm for solving this nonlinear program isdiscussed, and results of numerical tests are presented.