Boucher, Chris

A weak version of what is sometimes called the fundamental theorem of linear programming states that the extremal values of a linear function f(x,y)=ax+by over a convex polygonal region are attained at corners of the region. (Moreover, if an extremum is attained at two corners then it is attained everywhere on the line segment connecting them.) The...

Vuilleumier, Bernard

The shortest path between two points on the surface of a sphere is an arc of a great circle (great circle distance or orthodrome). On the Earth, meridians and the equator are great circles. Between any two points on a sphere that are not directly opposite each other, there is a unique great circle. The two points separate the great circle into two ...

Lauschke, Andreas

Interior point methods have taken the world of linear optimization by storm. Explore the path taken by an affine-scaling interior point method (a variant of Karmarkar's original 1984 primal projection method) for a simple linear optimization problem, defined by constraints, objective function, and initial point / Componente Curricular::Educação Sup...

Knobloch, J Lamb, JSW Webster, KN

We consider non-elementary T-points in reversible systems in R2n+1. We assume that the leading eigenvalues are real. We prove the existence of shift dynamics in the unfolding of this T-point. Furthermore, we study local bifurcations of symmetric periodic orbits occurring in the process of dissolution of the chaotic dynamics.

Torrence, Bruce

Attention gamers! You are a traveling salesman. Your task: visit the cities (represented as dots on the gameboard) one by one by clicking them. Start anywhere you like. You will trace out a route as you proceed. You must visit every city once and then return to your starting point. The goal is to find the shortest possible route that accomplishes t...

McLoone, Jon

The traveling salesman problem asks for the shortest route by which a salesman can visit a set of locations and return home. Drag the points to change the locations the salesman visits to see how the route changes / Componente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemática

Garza, Tomas

Fitting a straight line to a given collection of points in the plane may be accomplished using different criteria, the most commonly used being the minimization of the sum of the squares of the vertical distances from each point to the line (ordinary regression). Another criterion is to minimize the sum of the squares of the perpendicular distances...

Hu, Yifan

This Demonstration shows the optimal transport scheduling for two depots that are responsible for supplying building materials to seven construction sites. Given the amount of supply available at each depot and the demand at each site, the optimal scheduling minimizes the transport cost, assuming that the distance between a depot and the site is th...

Patacchini, FS Carrillo de la Plata, JA Huang, Y Wolansky, G

We study the numerical behaviour of a particle method for gradient ows involving linear and nonlinear di usion. This method relies on the discretisation of the energy via non- overlapping balls centred at the particles. The resulting scheme preserves the gradient ow structure at the particle level and enables us to obtain a gradient descent formula...

Wu, Frederick Lichtblau, Daniel

The traveling salesman problem (TSP) is an NP-complete problem. Different approximation algorithms have their advantages and disadvantages. Mathematica's function FindShortestTour offers a choice of four methods ("OrZweig", "OrOpt", "TwoOpt", "CCA"), which may yield identical results. This Demonstration provides another TSP algorithm called 3-Opt. ...