A new version of the ab initio gradient embedded genetic algorithm (GEGA) program for finding the global minima on the potential energy surface (PES) of mixed clusters formed by molecules and atoms is reported. The performance of the algorithm is demonstrated on the neutral H·(H(2)O)(n) (n = 1-4) clusters, that is, a radical H atom solvated in 1-4 water molecules. These clusters are of a fundam...

This is the first paper dealing with the study of weak sharp minima for constrained optimization problems on Riemannian manifolds, which are important in many applications. We consider the notions of local weak sharp minima, boundedly weak sharp minima, and global weak sharp minima for such problems and establish their complete characterizations in the case of convex problems on finite-dimensio...

A novel scheme is proposed for achieving motion segmentation in low-frame rate videos, with application to temporal super resolution. Probabilistic generative models are commonly used to perform unsupervised motion segmentation in videos. While they provide a general and elegant framework, they are hampered by severe local minima problems and often converge to inaccurate solutions, when there a...

A new algorithm is presented for the location of the global minimum of a multiple minima problem. It begins with a series of randomly placed probes in phase space, and then uses an iterative Gaussian redistribution of the worst probes into better regions of phase space until all probes converge to a single point. The method quickly converges, does not require derivatives, and is resistant to be...

One of the goals in molecular biology is to develop computational methods that can predict the native structures of proteins.{1} One approach{2-4} to this problem is to make use of the experimentally established fact that the native conformation of a protein is the thermodynamically most stable one.{5} Consequently, a useful approach is to search the potential energy space for the conformation ...

A space warping method, facilitating the modeling of large-scale conformational changes in mesoscopic systems, is presented. The method uses a set of "global (or collective) coordinates" that capture overall behavior, in conjunction with the set of atomic coordinates. Application of the space warping method to energy minimization is discussed. Several simulations where the method is used to det...

We locate putative global minima for (C60)N clusters modelled by the potential of Pacheco and Prates-Ramalho up to N=105. These minima are based on icosahedral packing up to N=15, but above this size the lowest-energy structures are decahedral or close-packed. Although structures based on the 98-molecule Leary tetrahedron, which have been inferred from experiment, are not lowest in energy for t...

The multiple-minima problem is a classical problem in molecular structure prediction. For ligand-receptor systems, a possible direction to alleviate this major obstacle is to simplify the objective function (intermolecular energy) and smooth its profile. We introduce long-distance atom-atom potentials for ligand-receptor interactions. The longer ranges result in averaging of the energy potentia...

The Griewank function is commonly used to test the ability of different solution procedures to find local optima. It is important to know the exact number of minima of the function to support its use as a test function. However, to the best of our knowledge, no attempts have been made to analytically derive the number of minima. Because of the complex nature of the function surface, a numerical...

This paper proposes and analyzes an asynchronously parallel optimization algorithm for finding multiple, highquality minima of nonlinear optimization problems. Our multistart algorithm considers all previously evaluated points when determining where to start or continue a local optimization run. Theoretical results show that, under certain assumptions, the algorithm almost surely starts a finit...