On the Delayed Weighted Gradient Method with Simultaneous Step-Size Search

Hugo Lara Urdaneta, Rafael Aleixo

Resumo


In this article it is presented a two step rst order algorithm, based on bidimensional minimization, to deal with convex quadratic optimization problems. Our analysis show linear convergence and A-orthogonality of the gradient iterates. Numerical experimentation show the eectiveness of our method.


Palavras-chave


Gradient methods; convex quadratic optimization; Krylov subspace methods; DWGM.

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Referências


R. Andreani and M. Raydan. Properties of the delayed weighted gradient method. In: Computational Optimization and Applications 78 (2021), pp. 167180. doi: 10.1007/ s10589-020-00232-9.

R. De Asmundis et al. An e cient gradient method using the Yuan steplength. In: Computational Optimization and Applications 59 (2014), pp. 541563. doi: 10.1007/s10589- 014-9669-5.

J. Barzilai and J. M. Borwein. Two-point step size gradient methods. In: IMA Journal of Numerical Analysis 8.1 (1988), pp. 141148. doi: 10.1093/imanum/8.1.141.

A. L. Cauchy. Méthode générale pour la résolution des systemes d'équations simultanées. In: Comptes Rendus Sci. Paris 25 (1847), pp. 536538.

Y. H. Dai, Y. Huang, and X. W. Liu. A family of spectral gradient methods for optimization. In: Computational Optimization and Applications 74 (2019), pp. 43 65. doi: 10.1007/ s10589-019-00107-8.

T. A. Davis and Y. Hu. The University of Florida Sparse Matrix Collection. In: ACM Trans. Math. Softw. 38.1 (2011). doi: 10.1145/2049662.2049663.

D. di Serano et al. On the steplength selection in gradient methods for unconstrained optimization. In: Applied Mathematics and Computation 318 (2018), pp. 176195. doi: 10.1016/j.amc.2017.07.037.

E. D. Dolan and J. J. Moré. Benchmarking optimization software with performance proles. In: Mathematical Programming 91 (2002), pp. 2012013. doi: 10.1007/s101070100263.

R. Fletcher. A limited memory steepest descent method. In: Mathematical Programming 135 (2012), pp. 413436. doi: 10.1007/s10107-011-0479-6.

G. Frassoldati, L. Zanni, and G. Zanghirati. New adaptive stepsize selections in gradient methods. In: Journal of Industrial & Management Optimization 4.2 (2008), pp. 299 312. doi: 10.3934/jimo.2008.4.299.

A. Friedlander et al. Gradient method with retards and generalizations. In: SIAM Journal on Numerical Analysis 36.1 (1999), pp. 275289. doi: 10.1137/S003614299427315X.

Y. Huang et al. Gradient methods exploiting spectral properties. In: Optimization Methods and Software 35.4 (2020), pp. 681705. doi: 10.1080/10556788.2020.1727476.

H. F. Oviedo-Leon. A delayed weighted gradient method for strictly convex quadratic minimization. In: Computational Optimization and Applications 74 (2019), pp. 729746. doi: 10.1007/s10589-019-00125-6.

T. Serani, G. Zanghirati, and L. Zanni. Gradient projection methods for large quadratic programs and applications in training support vector machines. In: Optimization Methods and Software 20 (2005), pp. 353378. doi: 10.1080/10556780512331318182.




DOI: https://doi.org/10.5540/03.2022.009.01.0288

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