Gradient-Based Optimization Algorithm for Solving Sylvester Matrix Equation

Juan Zhang and Xiao Luo
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Juan Zhang: Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, Xiangtan 411105, China
Xiao Luo: Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, China

Mathematics, 2022, vol. 10, issue 7, 1-14

Abstract: 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.

Keywords: Sylvester matrix equation; Kronecker product; adaptive accelerated proximal gradient method; Newton-accelerated proximal gradient method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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