A numerical computation on the structure of the roots of q-extension of Genocchi polynomials

AbstractIn this work we observe the behavior of real roots of the q-extension of Genocchi polynomials, cn,q(x), using numerical investigation. By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the cn,q(x) for −1<q<0. Finally, we give a table for the solutions of the q-extension of Genocchi polynomials

On the composition of convex envelopes for quadrilinear terms

International audienceWithin the framework of the spatial Branch-and-Bound algorithm for solving Mixed-Integer Nonlinear Programs, different convex relaxations can be obtained for multilinear terms by applying associativity in different ways. The two groupings ((x1x2)x3)x4 and (x1x2x3)x4 of a quadrilinear term, for example, give rise to two different convex relaxations. In [6] we prove that having fewer groupings of longer terms yields tighter convex relaxations. In this paper we give an alternative proof of the same fact and perform a computational study to assess the impact of the tightened convex relaxation in a spatial Branch-and-Bound setting

Bilateral teleoperation for linear force sensorless 3D robots

It is well known that for bilateral teleoperation, force feedback information is needed. In this paper, we propose a control approach for bilateral teleoperation with uncertainties in the model of the slave robot and which does not use force sensors for haptic feedback. The controller design is based on a cyclic switching algorithm. In the first phase of the cyclic algorithm, we estimate the environmental force acting on the slave robot and in the second phase a tracking controller ensures that the position of the slave robot is tracking the position of the master robot. A stability analysis of the overall closed-loop system is presented and the approach is illustrated by means of an example

On convex relaxations of quadrilinear terms

Quadrilinear, Trilinear, Bilinear, Convex relaxation, Reformulation, Global optimization, Spatial branch and bound, MINLP,