An accelerated first-order method with complexity analysis for solving cubic regularization subproblems
نویسندگان
چکیده
We propose a first-order method to solve the cubic regularization subproblem (CRS) based on novel reformulation. The reformulation is constrained convex optimization problem whose feasible region admits an easily computable projection. Our requires computing minimum eigenvalue of Hessian. To avoid expensive computation exact eigenvalue, we develop surrogate where replaced with approximate one. then apply methods such as Nesterov’s accelerated projected gradient (APG) and Barzilai-Borwein problem. As our main theoretical contribution, show that when $$\epsilon$$ -approximate computed by Lanczos approximately solved APG, approach returns solution CRS in $${\tilde{O}}(\epsilon ^{-1/2})$$ matrix-vector multiplications (where $${\tilde{O}}(\cdot )$$ hides logarithmic factors). Numerical experiments are comparable outperform Krylov subspace easy hard cases, respectively. further implement solvers adaptive methods, numerical results algorithms state-of-the-art algorithms.
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ژورنال
عنوان ژورنال: Computational Optimization and Applications
سال: 2021
ISSN: ['0926-6003', '1573-2894']
DOI: https://doi.org/10.1007/s10589-021-00274-7