We propose a new algorithmic approach for global optimization in protein folding. We use the information found in various local minima to direct the search for the global minimum. In this way, we explore the energy landscape efficiently by considering only the space of local minima instead of the whole feasible space of conformations. Our fundamental approach is to sample only the space of loca...

The aim of the paper is to present a new global optimization method for determining all the optima of the Least Squares Method (LSM) problem of pairwise comparison matrices. Such matrices are used, e.g., in the Analytic Hierarchy Process (AHP). Unlike some other distance minimizing methods, LSM is usually hard to solve because of the corresponding nonlinear and non-convex objective function. It...

In this paper, we propose a stochastic dynamic local search (SDLS) method for Multiple-Valued Logic (MVL) learning by introducing stochastic dynamics into the traditional local search method. The proposed learning network maintains some trends of quick descent to either global minimum or a local minimum, and at the same time has some chance of escaping from local minima by permitting temporary ...

An alternative strategy to find the minimal energy structure of nanoclusters is presented and implemented. We use it to determine the structure of metallic clusters. It consists in an unbiased search, with a global minimum algorithm: conformational space annealing. First, we find the minima of a many-body phenomenological potential to create a data bank of putative minima. This procedure assure...

The minima hopping algorithm (MHOP) to find global minima on potential energy surfaces is used for protein structure prediction. The energy surface of the protein is represented with an all-atom OPLS force field and an implicit free energy solvation term. The system we studied here is the small 10-residue beta-hairpin mini-protein, chignolin. Starting from a completely extended structure, we fo...

We show that there are no spurious local minima in the non-convex factorized parametrization of low-rank matrixrecovery from incoherent linear measurements. With noisy measurements we show all local minima are very close to aglobal optimum. Together with a curvature bound at saddle points, this yields a polynomial time global convergenceguarantee for stochastic gradient descent ...

A novel procedure is given here for constructing non-negative functions with zero-valued global minima coinciding with eigenvectors of a general real matrix A. Some of these functions are distinct because all their local minima are also global, offering a new way of determining eigenpairs by local optimization. Apart from describing the framework of the method, the error bounds given separately...

In this work we propose a general procedure for estimating the global minima of mathematical programs given in the general form as follows: min P0 (t) s.t. Pi (t) ≤ 0 for i = 1, . . . , k (Π) , where the functions Pi : R n → R are n-dimensional polynomials which are supposed to be non convex. The theory behind the Method of Moments guarantees that all global minima of the non convex program (Π)...

A novel procedure is given here for constructing non-negative functions with zerovalued global minima coinciding with eigenvectors of a general real matrix A. Some of these functions are distinct because all their local minima are also global, offering a new way for the determination of eigenpairs by local optimization. Beyond describing the framework of the method, the error bounds given separ...

We discuss a novel genetic algorithm that can be used to find global minima on the potential energy surface of disordered ceramics and alloys using a real-space symmetry adapted crossover. Due to a high number of symmetrically equivalent solutions of many alloys a conventional genetic algorithms using reasonable population sizes are unable to locate the global minima for even the smallest syste...