This letter investigates hybrid lower bounds on the mean square error in order to predict the so-called threshold effect. A new family of tighter hybrid large error bounds based on linear transformations (discrete or integral) of a mixture of the McAulay-Seidman bound and the Weiss-Weinstein bound is provided in multivariate parameters case with multiple test points. For use in applications, we...

In many iterative optimization methods, fixed-point theory enables the analysis of convergence rate via contraction factor associated with linear approximation operator. While this characterizes asymptotic convergence, it does not explain non-linear behavior these algorithms in non-asymptotic regime. letter, we take into account effect first-order error and present a closed-form bound on terms ...

Although there is an extensive literature on the maxima of Gaussian processes, are relatively few non-asymptotic bounds their lower-tail probabilities. The aim this paper to develop such a bound, while also allowing for many types dependence. Let (ξ1,…,ξN) be centered vector with standardized entries, whose correlation matrix R satisfies maxi≠jRij≤ρ0 some constant ρ0∈(0,1). Then, any ϵ0∈(0,1−ρ0...

In this paper we consider a two dimensional strip packing problem. The problem consists of packing a set of rectangular items in one strip of width W and infinite height. They must be packed without overlapping, parallel to the edge of the strip and we assume that the items are oriented, i.e. they cannot be rotated. To solve this problem, we use three exact methods: a branch and bound method, a...

Abstract Branch and Bound (B&B) algorithms in Global Optimization are used to perform an exhaustive search over the feasible area. One choice is use simplicial partition sets. Obtaining sharp cheap bounds of objective function a simplex very important construction efficient B&B algorithms. Although enclosing box implies overestimation, boxes more natural when dealing with individual coo...