Ernesto G. Birgin

PACKMOL: A package for building initial configurations for molecular dynamics simulations

Adequate initial configurations for molecular dynamics simulations consist of arrangements of molecules distributed in space in such a way to approximately represent the systems overall structure. In order that the simulations are not disrupted by large van der Waals repulsive interactions, atoms from different molecules must keep safe pairwise distances. Obtaining such a molecular arrangement can be considered a packing problem: Each type molecule must satisfy spatial constraints related to the geometry of the system, and the distance between atoms of different molecules must be greater than some specified tolerance. We have developed a code able to pack millions of atoms, grouped in arbitrarily complex molecules, inside a variety of three‐dimensional regions. The regions may be intersections of spheres, ellipses, cylinders, planes, or boxes. The user must provide only the structure of one molecule of each type and the geometrical constraints that each type of molecule must satisfy. Building complex mixtures, interfaces, solvating biomolecules in water, other solvents, or mixtures of solvents, is straightforward. In addition, different atoms belonging to the same molecule may also be restricted to different spatial regions, in such a way that more ordered molecular arrangements can be built, as micelles, lipid double‐layers, etc. The packing time for state‐of‐the‐art molecular dynamics systems varies from a few seconds to a few minutes in a personal computer. The input files are simple and currently compatible with PDB, Tinker, Molden, or Moldy coordinate files. The package is distributed as free software and can be downloaded from http://www.ime.unicamp.br/∼martinez/packmol/.

Nonmonotone Spectral Projected Gradient Methods on Convex Sets

Nonmonotone projected gradient techniques are considered for the minimization of differentiable functions on closed convex sets. The classical projected gradient schemes are extended to include a nonmonotone steplength strategy that is based on the Grippo--Lampariello--Lucidi nonmonotone line search. In particular, the nonmonotone strategy is combined with the spectral gradient choice of steplength to accelerate the convergence process. In addition to the classical projected gradient nonlinear path, the feasible spectral projected gradient is used as a search direction to avoid additional trial projections during the one-dimensional search process. Convergence properties and extensive numerical results are presented.

On Augmented Lagrangian Methods with General Lower-Level Constraints

Augmented Lagrangian methods with general lower-level constraints are considered in the present research. These methods are useful when efficient algorithms exist for solving subproblems in which the constraints are only of the lower-level type. Inexact resolution of the lower-level constrained subproblems is considered. Global convergence is proved using the constant positive linear dependence constraint qualification. Conditions for boundedness of the penalty parameters are discussed. The resolution of location problems in which many constraints of the lower-level set are nonlinear is addressed, employing the spectral projected gradient method for solving the subproblems. Problems of this type with more than

Algorithm 813: SPG—Software for Convex-Constrained Optimization

3 \times 10^6

Large-Scale Active-Set Box-Constrained Optimization Method with Spectral Projected Gradients

variables and

Augmented Lagrangian methods under the constant positive linear dependence constraint qualification

14 \times 10^6

Optimizing the packing of cylinders into a rectangular container: A nonlinear approach

constraints are solved in this way, using moderate computer time. All the codes are available at http://www.ime.usp.br/

Global minimization using an Augmented Lagrangian method with variable lower-level constraints

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Numerical Comparison of Augmented Lagrangian Algorithms for Nonconvex Problems

egbirgin/tango/.

Minimizing the object dimensions in circle and sphere packing problems

Fortran 77 software implementing the SPG method is introduced. SPG is a nonmonotone projected gradient algorithm for solving large-scale convex-constrained optimization problems. It combines the classical projected gradient method with the spectral gradient choice of steplength and a nonmonotone line-search strategy. The user provides objective function and gradient values, and projections onto the feasible set. Some recent numerical tests are reported on very large location problems, indicating that SPG is substantially more efficient than existing general-purpose software on problems for which projections can be computed efficiently.