  The main contribution of this thesis is the development of a new algorithm
for solving convex quadratic programs. It consists in combining the method of
multipliers with an infeasible active-set method. Our approach is iterative. In
each step we calculate an augmented Lagrange function. Then we minimize this
function using an infeasible active-set method that was already successfully
applied to similar problems. After this we update the Lagrange multiplier for
the equality constraints. Finally we try to solve convex quadratic program
directly, again with the infeasible active-set method, starting from the
optimal solution of the actual Lagrange function. Computational experience with
our method indicates that typically only few (most of the time only one) outer
iterations (multiplier-updates) and also only few (most of the time less than
ten) inner iterations (minimization of the Lagrange function) are required to
reach the optimal solution.
  The diploma thesis is organized as follows. We close this chapter with some
nota- tion used throughout. In Chapter 2 we show the equivalence of different
QP problem formulations and present some important so-called direct methods for
solving equality-constrained QPs. We cover the most important aspects for
practically successful interior point methods for linear and convex quadratic
programming in Chapter 3. Chapter 4 deals with ingredients for practically
efficient feasible active set methods. Finally Chapter 5 provides a close
description of our Lagrangian infeasible active set method and further gives a
convergence analysis of the subalgorithms involved.
