An Adaptive Memristor-Programming Neurodynamic Approach to Nonsmooth Nonconvex Optimization Problems

This article introduces an adaptive memristor-programming neurodynamic approach (AMPNA) to tackle optimization problems that are nonconvex and nonsmooth with inequality and equality constraints. In the circumstance that requiring neither estimating penalty parameters, nor the coerciveness of inequality constraints, the state of the AMPNA can go into the feasible region from any initial points within a finite amount of time and ultimately converge to the critical point set of the aforementioned optimization problem. Differ from the existing neurodynamic approach (NA), AMPNA has superiority in using memristor. On the one hand, with regard to power consumption, AMPNA makes the most of memristor's unconventional characteristics to execute within the flux-charge realm. Compared with conventional NA executing within the voltage-current realm, AMPNA executes within the flux-charge realm and consumes power only in the analog transient. Once the analog transient is complete, all voltages, currents and powers in the AMPNA disappear. On the other hand, in terms of result storage, since the memristor has the ability to calculate and save information at the same physical location, the AMPNA no longer needs additional memories, and can implement the calculation scheme by the principle of in-memory computation. Therefore, the AMPNA presented in this article has significant advantages in reducing power consumption and storage space. Finally, AMPNA's optimization capacity and exceptional performance are confirmed through numerical simulations.