Iterative Methods for MPC on Graphical Processing Units

The high oating point performance and memory bandwidth of Graphical Processing Units (GPUs) makes them ideal for a large number of computations which often arises in scientic computing, such as matrix operations. GPUs achieve this performance by utilizing massive par- allelism, which requires reevaluating existing algorithms with respect to this new architecture.

This is of particular interest to large-scale constrained optimization problems with real-time requirements. The aim of this study is to investigate dierent methods for solving large-scale optimization problems with focus on their applicability for GPUs. We examine published techniques for iterative methods in interior points methods (IPMs) by applying them to simple test cases, such as a system of masses connected by springs.

Iterative methods allows us deal with the ill-conditioning occurring in the later iterations of the IPM as well as to avoid the use of dense matrices, which may be too large for the limited memory capacity of current graphics cards.