On the approximate solution of a class of large discrete quadratic programming problems by ΔΣ modulation: the case of circulant quadratic forms

  • Authors:

  • Sergio Callegari;Federico Bizzarri;Riccardo Rovatti;Gianluca Setti

  • Affiliations:

  • Department of Electronics, Computer Sciences and Systems and Advanced Research Center on Electronic Systems for Information and Communication Technologies "E. De Castro", University of Bologna, Bo ...;Department of Electronics and Information, Polytechnic of Milan, Milan, Italy and Advanced Research Center on Electronic Systems for Information and Communication Technologies "E. De Castro", Univ ...;Department of Electronics, Computer Sciences and Systems and Advanced Research Center on Electronic Systems for Information and Communication Technologies "E. De Castro", University of Bologna, Bo ...;Department of Engineering, University of Ferrara, Italy and Advanced Research Center on Electronic Systems for Information and Communication Technologies "E. De Castro", University of Bologna, Bol ...

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 2010

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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.