Polynomial Linear Programming with Gaussian Belief Propagation

Interior-point methods are state-of-the-art algorithms for solving linear programming (LP) problems with polynomial complexity. Specifically, the Karmarkar algorithm typically solves LP problems in time O(n^{3.5}), where $n$ is the number of unknown variables. Karmarkar's celebrated algorithm is known to be an instance of the log-barrier method using the Newton iteration. The main computational overhead of this method is in inverting the Hessian matrix of the Newton iteration. In this contribution, we propose the application of the Gaussian belief propagation (GaBP) algorithm as part of an efficient and distributed LP solver that exploits the sparse and symmetric structure of the Hessian matrix and avoids the need for direct matrix inversion. This approach shifts the computation from realm of linear algebra to that of probabilistic inference on graphical models, thus applying GaBP as an efficient inference engine. Our construction is general and can be used for any interior-point algorithm which uses the Newton method, including non-linear program solvers.Comment: 7 pages, 1 figure, appeared in the 46th Annual Allerton Conference on Communication, Control and Computing, Allerton House, Illinois, Sept. 200

The world crisis: the implications of globalised finance

The term “globalisation” has survived its first significant sell-by date in modern times. Rightly, it continues to attract policy attention and debate at the very highest levels. Together with just a handful of others—economic growth and inequality, financial crisis, climate change—with all of which it remains inextricably intertwined, only globalisation among economic phenomena has both effects and causes observable from outer space. Its impact on the welfare of humanity is therefore singular. This is even before one considers the sweeping changes in culture and politics that ever greater global integration both requires and engenders. This article cannot hope to cover the massive body of modern thinking that surrounds globalisation. Instead, what it seeks to do is two-fold: first, flag, with the benefit of hindsight, some of the key background points that any continuing discussion of globalisation needs to keep in mind; and second, offer conjecture where the most likely contentious issues in the near future might be. To keep within space constraints, careful and exhaustive discussion of empirical evidence is omitted. Instead, just the largest salient facts are provided where needed

Comment on Donohue

A comment on John J. Donohue III\u27s article on the effects of fee-shifting rules on the rate of settlements in lawsuits is presented. The article bears out the idea that something may work fine in practice but it remains to be proven if it will work in theory