An adaptive memristive dynamical system to nonsmooth optimization problems

In this paper, an adaptive memristive dynamical system (AMDS) is proposed to address nonsmooth optimization problems with equality and inequality constraints. Two features distinguish our methods from the existing dynamical systems. First, an adaptive term is introduced into AMDS to ensure that the state from any initial point converges to the optimal solution of nonsmooth optimization problems, and avoids any prior calculation of penalty parameter. Second, from a physical standpoint, unlike traditional dynamical systems operating in the voltage–current domain, AMDS operates in the flux–charge domain. This effectively utilizes the atypical properties of the memristor over conventional dynamical systems. One of the greatest advantages is that AMDS operating in the flux–charge domain consumes power only during the analog transient, which significantly reduces power consumption. Moreover, no additional memory is required in AMDS, since the memristor can execute information calculation and storage at the same physical location. Finally, numerical examples are provided to demonstrate the advantages and optimization capacities of AMDS.