Two Matrix-Type Projection Neural Networks for Solving Matrix-Valued Optimization Problems
In recent years, matrix-valued optimization algorithms have been studied to enhance the computational performance of vector-valued optimization algorithms. This paper presents two matrix-type projection neural networks, continuous-time and discrete-time models, for solving matrix-valued optimization problems. The proposed continuous-time neural network may be viewed as a significant extension to the vector-type double projection neural network. More importantly, the proposed discrete-time projection neural network can be parallelly implemented in terms of matrix state space. Under pseudo-monotonicity condition and Lipschitz continuous condition, it is guaranteed that the two proposed matrix-type projection neural networks are globally convergent to the optimal solution. Finally, computed examples show that the two proposed matrix-type projection neural networks are much superior to the vector-type projection neural network in computation speed.
KeywordsMatrix-type neural network Matrix-valued optimization Global convergence Computation time
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