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A technique of convex quadratic programming and quadratic programming, which is applied in the field of time-varying quadratic programming problem solvers in the real number domain, and can solve problems such as unreasonable and difficult to satisfy
Active Publication Date: 2018-03-09
SOUTH CHINA UNIV OF TECH
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When the neural network is applied in the actual system, such a requirement is sometimes difficult to meet
In addition, in the actual system, the reciprocal of the inductance parameter value and the capacitan...
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Embodiment 1
[0076] Such as figure 1 Shown is a flow chart of a time-varying convex quadratic programming solver design method of an example of the present invention; a design of a time-varying convex quadratic programming solver design method comprises the steps:
[0077] 1) Standardize the actual physical system or numerical solution in the form of a time-varying quadratic programming problem through mathematical modeling methods, and establish a standard quadratic programming problem model for the system;
[0078] 2) According to the Lagrangian multiplier method, respectively obtain the partial derivative information about the optimal solution and the Lagrange multiplier of the standard time-varying quadratic programming problem in step 1), and write the Lagrangian optimization formula;
[0079] 3) Transform the partial derivative information about the optimal solution and the Lagrange multiplier in step 2) into a standard time-varying matrix form, and write the time-varying matrix equa...
Embodiment 2
[0138] In order to demonstrate the actual system design process, an example is used to illustrate the problem: Assume that the time-varying parameter matrix of the system has been obtained, and consider a time-varying quadratic programming problem model in the real number domain with the following time-varying matrix
[0144] According to formula (6), the above quadratic programming problem models (11)-(12) can be written in the following matrix equation form
[0145] W(t)Y(t)=G(t) (13)
[0146] in
[0147]
[0148] Y(t):=[x 1 (t) x 2 (t) λ(t)] T , G(t):=[-sin t -cos tcos 3t] T
[0149] According to the following implicit kinetic equation expression
[0150]
[0151] and to Definition
[0152] Y(t):=[x T (t),λ T (t)] T =[x 1 (t), x 2 (t),...,x n (t),λ 1 (t),λ 2 (t),...,λ m (t)] T (15)
[0153]The system...
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Abstract
The invention discloses a time-varying convex quadratic programming solver design method. The method includes steps: establishing a time-varying quadratic programming standard model of a practical physical system through mathematical modeling; according to the Lagrange multiplier method, subjecting the quadratic programming standard model to optimal value solving to acquire optimal solution and Lagrange's multiplier related partial derivative information; converting the partial derivative information into a standard time-varying matrix form; designing an error functional equation according tothe standard time-varying matrix; according to the error functional equation and a power type varying-parameter recurrent neural dynamic method, designing a time-varying quadratic programming problempower type solver in a real number field through a monotone increasing odd activation function, so that a network state obtained through the time-varying quadratic programming problem power type solver is the optimal solution to the practical physical system or numerical solution time-varying quadratic programming problems. The time-varying convex quadratic programming solver design method has global convergence characteristics, errors can be converged to zero at a super-exponential speed, and accordingly calculation speed is greatly increased.
Description
technical field [0001] The patent of the invention belongs to the design method of the solver of the time-varying quadratic programming problem in the real number domain, and in particular relates to a recursive neural dynamics method based on power-type variable parameters. Background technique [0002] Artificial Neural Network (ANN) is a research hotspot in the field of artificial intelligence since the 1980s. It abstracts the human brain neuron network from the perspective of information processing, establishes a simple model, and forms different networks according to different connection methods. In engineering and academia, it is often referred to directly as a neural network or a neural network. A neural network is an operational model consisting of a large number of nodes (or neurons) connected to each other. Each node (Node) represents a specific output function, called the activation function (Activation Function). Each connection between two nodes represents a ...
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