Derivaton of QUBO formulations for sparse estimation

01/11/2020

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by   Tomohiro Yokota, et al.

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We propose a quadratic unconstrained binary optimization (QUBO) formulation of the l1-norm, which enables us to perform sparse estimation in the Ising-type annealing methods including quantum annealing. The QUBO formulation is derived via the Legendre transformation and the Wolfe theorem, which have recently been employed in order to derive the QUBO formulations of ReLU-type functions. Furthermore, it is clarified that a simple application of the derivation method to the l1-norm case gives a redundant variable; finally a simplified QUBO formulation is obtained by removing the redundant variable.