An Infeasible Point Method for Minimizing the Lennard-Jones Potential

Minimizing the Lennard-Jones potential, the most-studied model problem for molecular conformation, is an unconstrained global optimization problem with a large number of local minima. In this paper, the problem is reformulated as an equality constrained nonlinear programming problem with only linear constraints. This formulation allows the solution to approached through infeasible configurations, increasing the basin of attraction of the global solution. In this way the likelihood of finding a global minimizer is increased. An algorithm for solving this nonlinear program is discussed, and results of numerical tests are presented.