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

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 incre...

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Bibliographic Details
Published in:Neural networks Vol. 190; p. 107698
Main Authors: Du, Sichun, Dong, Yu, Xiao, Pingdan, Wei, Zhengmiao, Hong, Qinghui
Format: Journal Article
Language:English
Published: United States Elsevier Ltd 01.10.2025
Subjects:
Algorithms
Circuit design
Computer Simulation
Linear and quadratic programming
Memristor
Neural Networks, Computer
Neurodynamics
Programming, Linear
Time Factors
Neurodynamics
Memristor
Linear and quadratic programming
Circuit design
ISSN:0893-6080, 1879-2782, 1879-2782
Online Access:Get full text
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Summary: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×, 115.871×, 8.387×, 3.241×, 21.623×, respectively, acceleration over traditional QP solvers. •A general QP analog solver based on neurodynamics and RRAM arrays flexibly solves LP/QP problems (including equality/inequality constraints) by configuring operational circuits. It delivers high efficiency for small-scale tasks and maintains scalability for large-scale scenarios, enabling multi-application optimization through conductance programming.•The theoretical analysis of the equivalent mapping between the solver and the optimal neural network has been completed.•The analog solver leverages parallelism through physical laws, such as Ohm’s and Kirchhoff’s law, to accelerate the solving LP/QP problems, enabling a one-step solution. Evaluations show high accuracy, 21.6× speedup, reduced complexity, and improved efficiency over traditional solvers.
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ISSN:0893-6080
1879-2782
1879-2782
DOI:10.1016/j.neunet.2025.107698