"Interval Analysis and Its Applications"
Attila Kozma, University of Szeged, Hungary
In my talk I intend to give an introduction to the world of intervals and its applications. Interval-based methods are widely used, among others for verifying the results of heuristic algorithms, theorem proof, solving differential equations and even for global optmization.
Firstly I would like to detail what I dealed with in my master thesis. Its aim was to solve a 2D circle packing problem with an approximation algorithm and to validate its results in a way. The different circle packing configurations can be represented by a system of nonlinear equations. This system ought to be solved by a method that gives a verified inclusion of the solution vector, if one exists. For this purpose I used the interval variant of Newton’s method for multivariate systems, which gives information about the existence and uniqueness of the solution.
Secondly a global optimization method will be presented that uses the inclusion functions. A Branch-and-Bound algorithm can be built to determine the global minima of an n-variable function on a certain box of its domain. Accelerating tests will be shown to make the exponential algorithm faster.
Slides
