Circuit Implementation of Proximal Projection Neural Networks for Composite Optimization Problems

Abstract

Existing circuits for composite optimization problems tend to ignore the structure of nonsmooth objectives and lead to less practicability. To this end, with a proximal projection neural network (PPNN) and an inertial proximal projection neural network (IPPNN), this paper presents two novel analog circuit frameworks in presence of a nonsmooth term, where the actions of neuron are simulated via a feedback loop formed by integrator, gradient estimate, proximal operator and other basic operation models. In our circiuts, it shows that the stable output voltages are mapped to optimal solutions. Considering the nonsmooth term as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{l}_{1}}$</tex-math></inline-formula> -norm, we further design an effective analog circuit of soft thresholding operator. Theoretically, it is proved that both PPNN-based and IPPNN-based analog circuit frameworks have stable output voltages in the sense that the value of electronic components meets a certain mild proportion. Finally, two examples are simulated on Multisim 14.0 platform to validate the effectiveness and practicability of the proposed analog circuits.