Past

We discuss a method for solving very large structured symmetric indefinite equation systems arising in optimization with interior point methods.

Many real-life economic models involve system dynamics, spatial distribution or uncertainty and lead to large-scale optimization problems. Such problems usually have a hidden structure: they are constructed by replication of some small generic block. The linear algebra subproblems which arise in optimization algorithms for such problems involve matrices which are not only sparse, but they additionally display a block-structure with many smaller blocks sparsely distributed in the large matrix.

We have developed a structure-exploiting parallel interior point solver for optimization problems. Its design uses object-orientated programming techniques. The progress OOPS (Object-Orientated Parallel Solver: http://www.maths.ed.ac.uk/~gondzio/parallel/solver.html) on a number of different computing platforms and achieves scalability on a number of different computing platforms. We illustrate its performance on a collection of problems with sizes reaching 10⁹ variables arising from asset liability management and portfolio optimization.

This is a joint work with Andreas Grothey.

Given a family of independent events in a probability space, the probability

that none of the events occurs is of course the product of the probabilities

that the individual events do not occur. If there is some dependence between the

events, however, then bounding the probability that none occurs is a much less

trivial matter. The Lov

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In Clarendon Lab