An Improved Recurrent Network for Online Equality-Constrained Quadratic Programming

Chen, Ke; Zhang, Zhaoxiang

doi:10.1007/978-3-319-49685-6_1

Cited by 3 publications

(1 citation statement)

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“…When coefficient A is non-singular, x(t) has an unique theoretical solution x * = A −1 b; when coefficient A is singular, linear equations (1) can have no solution or multiple solutions. A number of related problems such as matrix inversion [1], [2], [3], [4], [5], quadratic programming/minimisation [6], [7], [8], Sylvester equations [9], Lyapunov matrix equation [10], [11] and linear matrix equations AX(t)B = C [12], [13] can be transformed into linear equations (1) via vectorisation and Kronecker product [4]. Such a problem is widely encountered in other fields of science and engineering such as ridge regression in machine learning [14], [15], [16], [17], signal processing [18], optical flow in computer vision [19], [20], and robotic inverse kinematics [21], [22].…”

Section: Introductionmentioning

confidence: 99%

Implicit Gradient Neural Networks with a Positive-Definite Mass Matrix for Online Linear Equations Solving

Chen

2017

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Motivated by the advantages achieved by implicit analogue net for solving online linear equations, a novel implicit neural model is designed based on conventional explicit gradient neural networks in this letter by introducing a positive-definite mass matrix. In addition to taking the advantages of the implicit neural dynamics, the proposed implicit gradient neural networks can still achieve globally exponential convergence to the unique theoretical solution of linear equations and also global stability even under no-solution and multi-solution situations. Simulative results verify theoretical convergence analysis on the proposed neural dynamics.

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