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

Area of Science:

• Engineering and Scientific Computing
• Computational Mathematics
• Analog Electronics

Background:

• Traditional numerical methods for linear programming (LP) and quadratic programming (QP) face computational complexity challenges with increasing problem size.
• Real-time solutions for LP and QP are critical in various engineering and scientific applications.
• Existing solvers struggle with scalability and speed for complex optimization tasks.

Purpose of the Study:

• To introduce a general analog solver based on neurodynamic principles for real-time LP and QP problem resolution.
• To demonstrate a novel approach achieving closed-form solutions via physical-level computation.
• To enhance the efficiency and applicability of optimization problem solving in demanding domains.

Main Methods:

• Development of a general analog solver utilizing neurodynamic principles.
• Implementation of configurable modular analog circuits for diverse constraint handling.
• Leveraging continuous-time dynamics, inherent parallelism, and sub-microsecond convergence of analog computing.
• Validation through five PSPICE simulation test experiments.

Main Results:

• The proposed solver achieves closed-form solutions for LP and QP problems in a single step.
• Demonstrated average solution accuracy exceeding 99.9% for QP problems.
• Maintained over 93% robustness against circuit nonidealities like noise and device deviation.
• Achieved significant acceleration, ranging from 3.241× to 173.572×, compared to traditional QP solvers.

Conclusions:

• The neurodynamically grounded analog solver provides an efficient and robust alternative for real-time LP and QP optimization.
• The analog computing architecture offers substantial speedups and high accuracy, even under nonideal conditions.
• This approach holds promise for advancing computational efficiency in complex optimization tasks across science and engineering.