We consider the problem of global minimization of rational functions on IR (unconstrained case), and on an open, connected, semi-algebraic subset of IR, or the (partial) closure of such a set (constrained case). We show that in the univariate case (n = 1), these problems have exact reformulations as semidefinite programming (SDP) problems, by using reformulations introduced in the PhD thesis of...

This paper presents a global mesh optimization framework for 3D triangular meshes of arbitrary topology. The mesh optimization task is formulated as an energy minimization problem including data attached terms measuring the fidelity to the original mesh as well as a shape potential favoring high quality triangles. Since the best solution for vertex relocation is strongly related to the mesh con...

This paper considers the problem of modeling and extracting arbitrary deformable contours from noisy images. We propose a global contour model based on a stable and regenerative shape matrix, which is invariant and unique under rigid motions. Combined with Markov random field to model local deformations, this yields prior distribution that exerts influence over a global model while allowing for...

As distributed systems increase in size, the need for scalable algorithms becomes more and more important. We argue that in the context of system identification, an essential building block of any scalable algorithm is the ability to estimate local dynamics within a large interconnected system. We show that in what we term the “full interconnection measurement” setting, this task is easily solv...

A comprehensive methodology of extraction of optimal sets of logical rules using neural networks and global minimization procedures has been developed. Initial rules are extracted using density estimation neural networks with rectangular functions or multi-layered perceptron (MLP) networks trained with constrained backpropagation algorithm, transforming MLPs into simpler networks performing log...

This paper deals with a method of the radiation pattern determination of the directional antennas. The method combining both the functional minimization method and the Fourier iterative algorithm is based on the phaseless near-field measurement on two plane surfaces. The method is used for a reconstruction of the phase distribution on the aperture of the measured antenna, and for the determinat...

Decision Diagrams (DDs) are often used in VLSI CAD systems for efficient representation and manipulation of Boolean functions. The most popular data structure are reduced ordered Binary Decision Diagrams (BDDs) [Bry86,DB98], also called ROBDDs. They are part of almost all courses on function representation in VLSI CAD education. BDDs are very sensitive to the variable ordering, i.e. the size of...