Work

Convergence Rate of Greedy SR1 With Trust Region Method

Year: 2024

Type: article

Abstract: Recently, Greedy Quasi-Newton methods have attracted wide interests of some researchers for their explicit superlinear convergence rate. These algorithms which achieve rapid local convergence construct a matrix sequence to approximate the Hessian matrix of the objective function iteratively. This paper proposes an algorithm, GR-SR1-TR, which incorporate Greedy SR1 method with Trust Region framework and employs a new correction technique. We prove that the approximation matrix sequence has a linear descent property under the Frobenius-norm metric. Further, both the global convergence and an explicit superlinear rate are established. The effectiveness of GR-SR1-TR has been verified by preliminary numerical experiments.

Source: Highlights in Science Engineering and Technology

DOI: 10.54097/axh66s95

Authors: Yu Xia, Hao Wu

Language: English

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4403986413

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