We show that ΔΣ modulators can be interpreted as heuristic solvers for a particular class of optimization problems. Then, we exploit this theoretical result to propose a novel technique to deal with very large unconstrained discrete quadratic programming (UDQP) problems characterized by quadratic forms entailing a circulant matrix. The result is a circuit-based optimization 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 untreatable differential equations were solved by designing electronic circuits analog to them. The approach can return high quality suboptimal solutions even when many hundreds of variables are considered and proved faster than conventional empirical optimization techniques. Detailed examples taken from two different domains illustrate that the range of manageable problems is large enough to cover practical applications.
S. Callegari, F. Bizzarri, R. Rovatti, G. Setti (2010). On the Approximate Solution of a Class of Large Discrete Quadratic Programming Problems by Modulation: The Case of Circulant Quadratic Forms. IEEE TRANSACTIONS ON SIGNAL PROCESSING, 58, 6126-6139 [10.1109/TSP.2010.2071866].
On the Approximate Solution of a Class of Large Discrete Quadratic Programming Problems by Modulation: The Case of Circulant Quadratic Forms
CALLEGARI, SERGIO;ROVATTI, RICCARDO;
2010
Abstract
We show that ΔΣ modulators can be interpreted as heuristic solvers for a particular class of optimization problems. Then, we exploit this theoretical result to propose a novel technique to deal with very large unconstrained discrete quadratic programming (UDQP) problems characterized by quadratic forms entailing a circulant matrix. The result is a circuit-based optimization 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 untreatable differential equations were solved by designing electronic circuits analog to them. The approach can return high quality suboptimal solutions even when many hundreds of variables are considered and proved faster than conventional empirical optimization techniques. Detailed examples taken from two different domains illustrate that the range of manageable problems is large enough to cover practical applications.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.