The search for the global minimum of a molecular potential energy surface is a challenging problem. The molecular structure corresponding to the global minimum is of particular importance because it usually dictates both the physical and chemical properties of the molecule. The existence of an extremely large number of local minima, the number of which may increase exponentially with the size o...

We consider the problem of finding the unconstrained global minimum of a realvalued polynomial p(x) : Rn → R, as well as the global minimum of p(x), in a compact set K defined by polynomial inequalities. It is shown that this problem reduces to solving an (often finite) sequence of convex linear matrix inequality (LMI) problems. A notion of Karush–Kuhn–Tucker polynomials is introduced in a glob...

This paper considers the identification problem of continuous-time systems with unknown time delays from sampled input-output data. An iterative global separable nonlinear least-squares (GSEPNLS) method which estimates the time delays and transfer function parameters separably is derived, by using stochastic global-optimization technique to avoid convergence to a local minimum. Futhermore, the ...

Generalized Product (GPC) Codes, an unification of Product Codes and Integrated Interleaved (II) Codes, are presented. Applications for approaches requiring local and global parities are described. The more general problem of extending product codes by adding global parities is studied and an upper bound on the minimum distance of such codes is obtained. Codes with one, two and three global par...

The prediction of a protein's tertiary structure, given its amino acid sequence, is one of the intriguing problems in biophysics and computational biology. Anfinsen's thermodynamic hypothesis indicates that the tertiary structure of a protein is the minimum free-energy conformation 1. Based on Anfinsen's hypothesis, the protein structure predict-tion problem can be treated as a global optimizat...

The minimum sum-of-squared error clustering problem is shown to be a concave continuous optimization problem whose every local minimum solution must be integer. We characterize its local minima. A procedure of moving from a fractional solution to a better integer solution is given. Then we adapt Tuy’s convexity cut method to find a global optimum of the minimum sum-of-squared error clustering p...

Branch and bound methods for finding all solutions of a global optimization problem in a box frequently have the difficulty that subboxes containing no solution cannot be easily eliminated if they are close to the global minimum. This has the effect that near each global minimum, and in the process of solving the problem also near the currently best found local minimum, many small boxes are cre...

We extend the method of Ghasemi and Marshall [SIAM. J. Opt. 22(2) (2012), pp 460-473], to obtain a lower bound fgp,M for a multivariate polynomial f(x) ∈ R[x] of degree ≤ 2d in n variables x = (x1, . . . , xn) on the closed ball {x ∈ Rn : ∑ x2d i ≤ M}, computable by geometric programming, for any real M . We compare this bound with the (global) lower bound fgp obtained by Ghasemi and Marshall, ...

We describe deterministic and randomized algorithms for finding global minimum cuts in undirected graphs. 1 Global and s-t cuts in undirected graphs Let G = (V,E,w) be a weighted undirected graph, where w : E → R is a weight (or cost, or capacity) function defined on its edges. A (global) cut (S, T ) of G is a partition of V into two disjoint non-empty sets, i.e., S, T 6= φ and S ∩ T = φ. Edges...

A new type of dynamical behavior of a multistable system is reported. We found that a simple non-equilibrium system can reduce its effective temperature autonomously at a global minimum if the residual frustration at a global minimum is small enough, which highlights an unexpected feature of non-equilibrium multistable