A modular system of algorithms for unconstrained minimization
ACM Transactions on Mathematical Software (TOMS)
Concurrent stochastic methods for global optimization
Mathematical Programming: Series A and B
Recent advances in global optimization
The Effective Energy Transformation Scheme as a General Continuation Approach to Global Optimization with Application to Molecular Conformation
A Trust-Region Algorithm for Global Optimization
Computational Optimization and Applications
A note on global optimization via the heat diffusion equation
Journal of Global Optimization
Learning mixture models via component-wise parameter smoothing
Computational Statistics & Data Analysis
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Strategies involving smoothing of the objective function have been used to help solve difficult global optimization problems arising in molecular chemistry. This paper proposes a new smoothing approach and examines some basic issues in smoothing for molecular configuration problems. We first propose a new, simple algebraic way of smoothing the Lennard-Jones energy function, which is an important component of the energy in many molecular models. This simple smoothing technique is shown to have close similarities to previously-proposed, spatial averaging smoothing techniques. We also present some experimental studies of the behavior of local and global minimizers under smoothing of the potential energy in Lennard-Jones problems. An examination of minimizer trajectories from these smoothed problems shows significant limitations in the use of smoothing to directly solve global optimization problems.