The Minima Hopping global optimization method uses physically realizable molecular dynamics moves in combination with an energy feedback that guarantees the escape from any potential energy funnel. For the purpose of finding reaction pathways, we argue that Minima Hopping is particularly suitable as a guide through the potential energy landscape and as a generator for pairs of minima that can b...

We propose a derivative-free algorithm for finding high-quality local minima for functions that require significant computational resources to evaluate. Our algorithm efficiently utilizes the computational resources allocated to it and also has strong theoretical results, almost surely starting a finite number of local optimization runs and identifying all local minima. We propose metrics for m...

In deep learning, depth, as well as nonlinearity, create non-convex loss surfaces. Then, does depth alone create bad local minima? In this paper, we prove that without nonlinearity, depth alone does not create bad local minima, although it induces non-convex loss surface. Using this insight, we greatly simplify a recently proposed proof to show that all of the local minima of feedforward deep l...

In many applications of terrain analysis, pits or local minima are considered artifacts that must be removed before the terrain can be used. Most of the existing methods for local minima removal work only for raster terrains. In this paper we consider algorithms to remove local minima from polyhedral terrains, by modifying the heights of the vertices. To limit the changes introduced to the terr...

We study inequalities that simultaneously relate the number of lattice points, volume and successive minima a convex body to one another. One main ingredient in order establish these relations is Blaschke's shaking procedure, by which problem can be reduced from arbitrary bodies anti-blocking bodies. As consequence our results, we obtain an upper bound on point enumerator terms minima, equivale...

We demonstrate the efficiency of the multidomain sampler (MDS) in finding multiple distinct global minima and low-energy local minima in the hydrophobic-polar (HP) lattice protein model. Extending the idea of partitioning energy space in the Wang-Landau algorithm, our approach introduces an additional partitioning scheme to divide the protein conformation space into local basins of attraction. ...