This article introduces a new class of memristor neural networks (NNs) for solving, in real-time, quadratic programming (QP) and linear programming (LP) problems. The networks, which are called memristor programming NNs (MPNNs), use a set of filamentary-type memristors with sharp memristance transitions for constraint satisfaction and an additional set of memristors with smooth memristance transitions for memorizing the result of a computation. The nonlinear dynamics and global optimization capabilities of MPNNs for QP and LP problems are thoroughly investigated via a recently introduced technique called the flux–charge analysis method. One main feature of MPNNs is that the processing is performed in the flux–charge domain rather than in the conventional voltage–current domain. This enables exploiting the unconventional features of memristors to obtain advantages over the traditional NNs for QP and LP problems operating in the voltage–current domain. One advantage is that operating in the flux–charge domain allows for reduced power consumption, since in an MPNN, voltages, currents, and, hence, power vanish when the quick analog transient is over. Moreover, an MPNN works in accordance with the fundamental principle of in-memory computing, that is, the nonlinearity of the memristor is used in the dynamic computation, but the same memristor is also used to memorize in a nonvolatile way the result of a computation.

中文翻译：

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用于线性和二次规划问题的忆阻器神经网络


本文介绍了一类新型忆阻器神经网络 (NN)，用于实时解决二次规划 (QP) 和线性规划 (LP) 问题。这些网络被称为忆阻器编程神经网络（MPNN），使用一组具有尖锐忆阻转变的丝状忆阻器来满足约束条件，并使用一组具有平滑忆阻转变的附加忆阻器来存储计算结果。 MPNN 对于 QP 和 LP 问题的非线性动力学和全局优化能力通过最近引入的称为通量-电荷分析方法的技术进行了彻底研究。 MPNN 的一个主要特点是处理是在磁通-电荷域而不是传统的电压-电流域中进行的。这使得能够利用忆阻器的非常规特性，在电压-电流域中运行的 QP 和 LP 问题上获得优于传统神经网络的优势。优点之一是在磁通电荷域中运行可以降低功耗，因为在 MPNN 中，当快速模拟瞬态结束时，电压、电流以及功率都会消失。此外，MPNN的工作原理符合内存计算的基本原理，即在动态计算中使用忆阻器的非线性，但同样的忆阻器也用于以非易失性方式存储计算结果。