Gradient-Based Optimization Algorithm for Solving Sylvester Matrix Equation

In this paper, we transform the problem of solving the Sylvester matrix equation into an optimization problem through the Kronecker product primarily. We utilize the adaptive accelerated proximal gradient and Newton accelerated proximal gradient methods to solve the constrained non-convex minimizati...

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Vydáno v:Mathematics (Basel) Ročník 10; číslo 7; s. 1040
Hlavní autoři: Zhang, Juan, Luo, Xiao
Médium: Journal Article
Jazyk:angličtina
Vydáno: Basel MDPI AG 01.04.2022
Témata:
adaptive accelerated proximal gradient method
Algorithms
Control theory
Dynamical systems
Iterative methods
Kronecker product
Methods
Newton-accelerated proximal gradient method
Numerical analysis
Optimization
Sylvester matrix equation
ISSN:2227-7390, 2227-7390
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Shrnutí:In this paper, we transform the problem of solving the Sylvester matrix equation into an optimization problem through the Kronecker product primarily. We utilize the adaptive accelerated proximal gradient and Newton accelerated proximal gradient methods to solve the constrained non-convex minimization problem. Their convergent properties are analyzed. Finally, we offer numerical examples to illustrate the effectiveness of the derived algorithms.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math10071040