It has been recently advocated that in large communication systems it is beneficial both for the users and for the network as a whole to store content closer to users. One particular implementation of such an approach is to co-locate caches with wireless base stations. In this paper we study geographically distributed caching of a fixed collection of files. We model cache placement with the hel...

This chapter reviews randomization algorithms developed in the last few years to solve a wide range of geometric optimization problems. We review a number of general techniques, including randomized binary search, randomized linear-programming algorithms, and random sampling. Next, we describe several applications of these techniques, including facility location, proximity problems, nearest nei...

Global optimization remains an important area of active research. Many macroscopic and microscopic applications in science and engineering still present formidable challenges to current global optimization techniques. In this work, a completely different, novel and general geometric framework for continuous global optimization is described. The proposed methodology is based on intelligent movem...

We discuss implementation of algorithms for constrained optimization, based on CLOS objects representing standard mathematical abstractions like affine spaces, vectors , and linear transformations. These abstractions simplify using the optimization library in varied applications, facilitate animation, carry no significant performance penalty (compared to traditional Fortran implementations). Ou...

In this paper, Bayesian nonlinear filtering is considered from the viewpoint of information geometry and a novel filtering method is proposed based on information geometric optimization. Under the Bayesian filtering framework, we derive a relationship between the nonlinear characteristics of filtering and the metric tensor of the corresponding statistical manifold. Bayesian joint distributions ...

This paper discusses geometric programs with joint probabilistic constraints. When the stochastic parameters are normally distributed and independent of each other, we approximate the problem by using piecewise polynomial functions with non-negative coefficients, and transform the approximation problem into a convex geometric program. We prove that this approximation method provides a lower bou...

Given a Euclidean graph G in Rd with n vertices and m edges, we consider the problem of adding an edge to G such that the stretch factor of the resulting graph is minimized. Currently, the fastest algorithm for computing the stretch factor of a graph with positive edge weights runs in O(nm+n2 log n) time, resulting in a trivial O(n3m+n4 log n) time algorithm for computing the optimal edge. Firs...

This paper presents a new methodology to establish the best global match of objects’ contours in images. The first step is the extraction of the sets of ordered points that define the objects’ contours. Then, by using the curvature value and its distance to the corresponded centroid for each point, an affinity matrix is built. This matrix contains information of the cost for all possible matche...

Abstract. Robust measures are introduced for methods to determine statistically uncorrelated or also statistically independent components spanning data measured in a way that does not permit direct separation of these underlying components. Because of the nonlinear nature of the proposed methods, iterative primal-dual based methods are presented for the optimization of merit functions, and conv...

There is an optimization method for the geometric correction of Landsat images, which uses a simulated direct solar irradiance image made from a digital elevation model (DEM) and a solar direction to determine parameters of the geometric transfer equations. The optimization method is quite simple, and also allows us high accuracy geometric correction in sub-pixel order. However, promising in pr...