Generalized nesterov’s algorithm for constrained minimization problems on closed convex sets

https://doi.org/10.31130/ud-jst.2023.506E

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Author

  • Pham Quy Muoi
    The University of Danang – University of Science and Education, Danang, Vietnam
    Vo Quang Duy
    The University of Danang – University of Science and Education, Danang, Vietnam
    Phan Duc Tuan
    The University of Danang – University of Science and Education, Danang, Vietnam

Từ khóa:

Constrained minimization problem
Closed convex set
Nesterov’s algorithm
Convergence
Convergence rate

Tóm tắt

In this paper, we propose a generalized Nesterov algorithm for the constrained optimization problems on a closed convex set. We prove the convergence as well as the convergence rate of the proposed algorithm. First, we present a new algorithm based on the generalization of Nesterov’s algorithm. Then, we prove the convergence as well as the convergence rate of the new algorithm. With a specific choice of parameters, the new algorithm becomes Nesterov’s algorithm. Therefore, the convergence as well as the convergence rate of Nesterov’s algorithm are also followed. We illustrate the effectiveness of the new algorithm as well as compare it with Nesterov’s algorithm and the gradient descent algorithm through a specific example.

Tài liệu tham khảo

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Đã Xuất bản

Dec 31, 2023
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Cách trích dẫn
Muoi, P. Q., V. Q. Duy, và P. D. Tuan. “Generalized nesterov’s Algorithm for Constrained Minimization Problems on Closed Convex Sets”. Tạp Chí Khoa học Và Công nghệ - Đại học Đà Nẵng, vol 21, số p.h 12.1, Tháng Chạp 2023, tr 90-94, doi:10.31130/ud-jst.2023.506E.

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