A Memristor-Based Analog Accelerator for Solving Quadratic Programming Problems

Quadratic programming (QP) problems are common in many applications requiring optimization, including automatic control systems, finance analysis, chemical processes, etc. Typical QP problems are solved digitally via an iterative algorithm with userdefined error tolerance for the final solution $[1,2]$. Consequently, the solution accuracy of QP solvers naturally tradeoffs with the latency, i.e., the time required to derive an acceptable solution. When both high accuracy and low latency are demanded, conventional digital QP solvers can be infeasible or impose a significant overhead. Alternatively, analog QP solvers [3], [4] have been shown to potentially reduce the latency while maintaining the same accuracy. However, the existing designs necessitate the use of capacitors in the circuit to implement constraint functions, which limits the extent of latency reduction and still yields latency in the order of milliseconds due to the capacitor charging time. In [5], a discrete analog QP solver was implemented on a PCB, and a resistive crossbar array was adopted to solve the targeted cost function without additional capacitors and reduce the computing time to $80 \mu \mathrm{s}$. Nonetheless, the digital potentiometers used in the design had poor linearity and hence degraded solution accuracy. Furthermore, the use of bulky digital potentiometers and excessive power/area consumption prevent the solver from real-time power/area-constrained applications where high accuracy, low latency, and low cost are needed.