An open source object oriented platform for rapid design of high performance path following interior-point methods

Abstract

<p> Interior point methods (IPMs) is a powerful tool in convex optimization. From the theoretical point of view, the convex set of feasible solutions is represented by a so-called barrier functional and the only information required by the algorithms is the evaluation of the barrier, its gradient and Hessian. As a result, IPM algorithms can be used for many types of convex problems and their theoretical performance depends on the properties of the barrier. In practice, performance depends on how the data structure is exploited at the linear algebra level. In this thesis, we make use of the object-oriented paradigm supported by C++ to create a platform where the aforementioned generality of IPM algorithms is valued and the possibility to exploit the data structure is available. We will illustrate the power of such an approach on optimization problems arrising in the field of Radiation Therapy, in particular Intensity Modulated Radiation Therapy. </p>