| Composite optimization problems are an important branch of optimization problems which are widely existing in the fields of compressed perception,image processing,ma-chine learning and others.Meanwhile,a number of novel optimization tools and effec-tive optimization algorithms have been born during the past years.Neural networks,as one of them,have been favored by researchers because of their simple structure,parallel computing capability,strong global optimization-seeking ability,adaptability,and wide applicability,etc.Note that traditional computer processors are no longer able to meet the computing performance demands with the increasing scale and complexity of neu-ral networks.Therefore,new solutions are greatly desired to enhance the computational power and efficiency of the algorithms.In this paper,we investigate the hardware im-plementation of a class of neural network algorithms for solving composite optimization problems.Analog circuits are designed to achieve the function of algorithm and the dy-namical behavior of the algorithm is simulated by varying the voltage values.Moreover,the feasibility of the designed circuits is verified.The main works of this paper are as follows:（1）The circuit implementation of the proximal operator is studied.Note thar the prox-imal operator can been transformed into soft thresholding operator which is innovatively designed with analog circuits by taking advantage of the“single-wire”nature of diodes.And its function as a soft threshold operator is verified by simulation.（2）For the composite optimization problem in which the objective function is con-vex and contains a nonsmooth term,a feedback loop formed by the integration module,the gradient calculation module,and the proximal operator mode module is used to simu-late the neuron behavior.An analog circuit framework based on the Proximal Projection Neural Network（PPNN）algorithm is designed.Firstly,the design process of the circuit is described,then,the equivalence of circuit and algorithm is derived and the stability and convergence of the output voltage of the circuit is demonstrated.Finally,two simulation experiments are performed.Example 1 is is a composite optimization problem involving quadratic polynomials and l1-norm.The output voltage is compared with the simulation results on Matlab,and the relative error is calculated to verify the stability of the designed circuit.Example 2 is a sparse signal recovery problem in compressed sensing.It is veri-fied that the designed circuit has practical applications by comparing experimental results on two platforms and analyzing the error.（3）A circuit framework based on the Inertial Proximal Projection Neural Network（IPPNN）algorithm is designed to compensate for the inability of PPNN-based circuits in finding locally optimal solutions when solving nonconvex composite optimization prob-lems.And it is proved that the circuit has a stable output voltage.A nonconvex nons-mooth composite optimization problem is solved by the designed circuit and it is proven that the circuit has the ability to find local optimal solutions through experimental simula-tion results.Next,the performance of the circuit is investigated.Firstly,the effect of the variation of electronic component parameters on the accuracy and convergence speed of the output voltage is studied.Then,the output voltages are compared with different initial conditions.Finally,the robustness of the designed circuit is verified by adding a thermal noise source.It is verified that the circuit we designed has good stability and robustness in solving nonconvex,nonsmooth composite optimization problems by these three sets of comparison experiments. |
