On the Approximate Solution of a Class of Large Discrete Quadratic Programming Problems by Delta Sigma Modulation: The Case of Circulant Quadratic Forms

We show that modulators can be interpreted as heuristic solvers for a particular class of optimisation problems. Then, we exploit this theoretical result to propose a novel technique to deal with very large Unconstrained Discrete Quadratic Programming (UDQP) problems characterised by quadratic forms entailing a circulant matrix. The result is a circuit based optimisation approach involving a recast of the original problem into signal processing specifications, then tackled by the systematic design of an electronic system. This is reminiscent of analog computing, where untractable differential equations were solved by designing electronic circuits analogue to them. The approach can return high quality sub-optimal solutions even when many hundreds of variables are considered and proved faster than conventional empirical optimisation techniques. Detailed examples taken from two different domains illustrate that the range of manageable problems is large enough to cover practical applications.