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Gradient-Based Optimization Algorithm for Solving Sylvester Matrix Equation

Author

Listed:
  • 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)

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.

Suggested Citation

  • Juan Zhang & Xiao Luo, 2022. "Gradient-Based Optimization Algorithm for Solving Sylvester Matrix Equation," Mathematics, MDPI, vol. 10(7), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1040-:d:778549
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    Citations

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    Cited by:

    1. Zhiguo Tan, 2022. "Fixed-Time Convergent Gradient Neural Network for Solving Online Sylvester Equation," Mathematics, MDPI, vol. 10(17), pages 1-13, August.

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