Adaptive cyclic gradient methods with interpolation

Yixin Xie, Cong Sun () and Ya-Xiang Yuan
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Yixin Xie: Beijing University of Posts and Telecommunications (BUPT)
Cong Sun: Beijing University of Posts and Telecommunications (BUPT)
Ya-Xiang Yuan: Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences

Computational Optimization and Applications, 2025, vol. 92, issue 1, No 9, 325 pages

Abstract: Abstract Gradient method is an important method for solving large scale problems. In this paper, a new gradient method framework for unconstrained optimization problem is proposed, where the stepsize is updated in a cyclic way. The Cauchy step is approximated by the quadratic interpolation. And the cycle for stepsize update is adjusted adaptively. Combining with the adaptive nonmonotone line search technique, we prove the global convergence of the proposed method. Furthermore, its sublinear convergence rate for convex problems and R-linear convergence rate for problems with quadratic functional growth property are analyzed. Numerical results show that our proposed algorithm enjoys good performances in terms of both computational cost and obtained function values.

Keywords: Gradient method; Unconstrained optimization; Quadratic interpolation; Linear convergence rate (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10589-025-00691-y

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