Geodesic
Optimization of subgradient method parameters on the base of rank-two correction of~metric~matrices
Diskretnyj analiz i issledovanie operacij, Tome 29 (2022) no. 3, pp. 24-44

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We establish a relaxation subgradient method (RSM) that includes parameter optimization utilizing metric rank-two correction matrices with a structure analogous to quasi-Newtonian (QN) methods. The metric matrix transformation consists of suppressing orthogonal and amplifying collinear components of the minimal length subgradient vector. The problem of constructing a metric matrix is formulated as a problem of solving an involved system of inequalities. Solving such system is based on a new learning algorithm. An estimate for its convergence rate is obtained depending on the parameters of the subgradient set. A new RSM has been developed and investigated on this basis. Computational experiments on complex large-scale functions confirm the effectiveness of the proposed algorithm. Tab. 4, bibliogr. 32.
Keywords: convex optimization, nonsmooth optimization, relaxation subgradient method. 
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     author = {V. N. Krutikov and P. S. Stanimirovi\'c and O. N. Indenko and E. M. Tovbis and L. A. Kazakovtsev},
     title = {Optimization of subgradient method parameters on the base of rank-two correction of~metric~matrices},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {24--44},
     publisher = {mathdoc},
     volume = {29},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2022_29_3_a2/}
}
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V. N. Krutikov; P. S. Stanimirović; O. N. Indenko; E. M. Tovbis; L. A. Kazakovtsev. Optimization of subgradient method parameters on the base of rank-two correction of~metric~matrices. Diskretnyj analiz i issledovanie operacij, Tome 29 (2022) no. 3, pp. 24-44. http://geodesic.mathdoc.fr/item/DA_2022_29_3_a2/