Discrete Programming Entailing Circulant Quadratic Forms: Refinement of a Heuristic Approach Based on ΔΣ Modulation

A recent result on the potential of Delta !Sigma modulators ( Delta !Sigma Ms) as heuristic optimizers for circulant unconstrained discrete quadratic programming (C-UDQP) is revisited, bridging it with current developments on the design of Delta !Sigma Ms by semi-definite programming (SDP). This provides an efficient strategy by which one can design a Delta !Sigma ext{M} and its input signal from a C-UDQP specification so that the solution of the C-UDQP problem can be found in the Delta !Sigma ext{M} output, all with almost no manual intervention. The proposed concept is validated by simulation-based experiments on a benchmark case, comparing the new strategy to previous results and exact optimization techniques.