Greedy PSB methods with explicit superlinear convergence

Zhen-Yuan Ji () and Yu-Hong Dai ()
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Zhen-Yuan Ji: Chinese Academy of Sciences
Yu-Hong Dai: Chinese Academy of Sciences

Computational Optimization and Applications, 2023, vol. 85, issue 3, No 4, 753-786

Abstract: Abstract Recently, Rodomanov and Nesterov proposed a class of greedy quasi-Newton methods and established the first explicit local superlinear convergence result for Quasi-Newton type methods. In this paper, we study a variant of Powell-Symmetric-Broyden (PSB) updates based on the greedy strategy. Firstly, we give explicit condition-number-free superlinear convergence rates of proposed greedy PSB methods. Secondly, we prove the global convergence of greedy PSB methods by applying the trust-region framework. One advantage of this result is that the initial Hessian approximation can be chosen arbitrarily. Thirdly, we analyze the behaviour of the randomized PSB method, that selects the direction randomly from any spherical symmetry distribution. Finally, preliminary numerical experiments illustrate the efficiency of proposed PSB methods compared with the standard SR1 method and PSB method. Our results are given under the assumption that the objective function is a strongly convex function, and its gradient and Hessian are Lipschitz continuous.

Keywords: Quasi-Newton methods; Powell’s Symmetric Broyden methods; Superlinear convergence; Global convergence (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10589-023-00495-y

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