In this work, different global optimization techniques are assessed for the automated development of molecular force fields, as used in molecular dynamics and Monte Carlo simulations. The quest of finding suitable force field parameters is treated as a mathematical minimization problem. Intricate problem characteristics such as extremely costly and even abortive simulations, noisy simulation re...

This paper describes a new optimization procedure called Diffusion which can be used in global circuit placement for suppressing inter-module and module-to-chip boundary overlaps. A salient feature of the proposed Diffusion procedure is that multiple decisions on the moves of all variables (module positions) are simultaneously made such that a global, analytic objective function is minimized. V...

Medical image segmentation requires consensus ground truth segmentations to be derived from multiple expert annotations. A novel approach is proposed that obtains consensus segmentations from experts using graph cuts (GC) and semi supervised learning (SSL). Popular approaches use iterative Expectation Maximization (EM) to estimate the final annotation and quantify annotator’s performance. Such ...

In this paper an optimization approach is used to solve the problem of nding the minimum distance between concave objects, without the need for partitioning the objects into convex sub-objects. Since the optimization problem is not unimodal (i.e., has more than one local minimum point), a global optimization technique, namely a Genetic Algorithm, is used to solve the concave problem. In order t...

Maximum likelihood estimation is one of the most used methods in quantum state tomography, where the aim is to find the best density matrix for the description of a physical system. Results of measurements on the system should match the expected values produced by the density matrix. In some cases however, if the matrix is parameterized to ensure positivity and unit trace, the negative log-like...

The problems of circumscribing and inscribing convex polygons with, respectively, minimum and maximum area k-gons have been studied extensively in the recent past because of their applications to robotics and collision avoidance problems [CY, DA]. In particular, Klee and Laskowski [KL] have given an O(n log%) algorithm for finding all local minima (with respect to area) among the triangles that...

We consider the problem of learning a one-hidden-layer neural network: we assume the input x ∈ R is from Gaussian distribution and the label y = a>σ(Bx) + ξ, where a is a nonnegative vector in R with m ≤ d, B ∈ Rm×d is a full-rank weight matrix, and ξ is a noise vector. We first give an analytic formula for the population risk of the standard squared loss and demonstrate that it implicitly atte...

Protein folding is a very difficult global optimization problem. Furthermore it is coupled with the difficult task of designing a reliable force field with which one has to search for the global minimum. A summary of a series of optimization methods developed and applied to various problems involving polypeptide chains is described in this paper. With recent developments, a computational treatm...

The classical simplex method is extended into the Semiglobal Simplex (SGS) algorithm. Although SGS does not guarantee finding the global minimum, it affords a much more thorough exploration of the local minima than any traditional minimization method. The basic idea of SGS is to perform a local minimization in each step of the simplex algorithm, and thus, similarly to the Convex Global Underest...