A general analog solver of linear and quadratic programming in one step

Abstract

Real-time solving of linear programming (LP) and quadratic programming (QP) problems faces critical demand across engineering and scientific domains. Conventional numerical approaches suffer from exponential growth in computational complexity as problem dimensionality and structural complexity increase. To address this challenge, we present a general analog solver grounded in neurodynamic principles, achieving closed-form solutions for both LP and QP through physical-level computation in one step. The proposed solver achieves the solution of LP/QP problems under diverse constraints through configurable interconnections of modular analog circuits. The analog computing architecture based on continuous-time dynamics leverages its inherent parallelism and sub-microsecond convergence properties to enhance the efficiency of optimization problem solving. Through five PSPICE simulation test experiments, the proposed QP solver achieved an average solution accuracy exceeding 99.9%, with robustness metrics maintaining over 93% precision when subjected to circuit nonidealities, including noise, parasitic resistance, and device deviation. Comparative analysis shows that the proposed solver demonstrates 173.572$\times$, 115.871$\times$, 8.387$\times$, 3.241$\times$, 21.623$\times$, respectively, acceleration over traditional QP solvers.