Issues of implementation of a library for parallel interior-point methods for quadratic programming are addressed. The solver can easily exploit any special structure of the underlying optimization problem. In particular, it allows a nested embedding of structures and by this means very complicated real-life optimization problems can be modeled. The efficiency of the solver is illustrated on several problems arising in the financial planning, namely in the asset and liability management. The problems are modeled as multistage decision processes and by nature lead to specially structured tree-sparse problems. By taking the variance of the random variables into account the problems become nonseparable quadratic programs. A reformulation of the problem is proposed which reduces density of matrices involved and by these means significantly simplifies its solution by an interior point method. The object-oriented parallel solver achieves high efficiency by careful exploitation of the block sparsity of these problems. As a result a problem with 10 million decision variables is solved in less than 2 hours on a serial computer. The approach is by nature scalable and the parallel implementation achieves perfect speed-ups.
Technical report MS-03-001, School of Mathematics, University of Edinburgh, Edinburgh, UK, April 2003