Improvement of information technology on the basis of method of metric proximal gradient with introduction of diagonal step

DOI: 10.31673/2412-9070.2021.063540

Abstract

The article presents some aspects of the use of optimization methods in telecommunications networks. The use of optimization methods by means of machine learning is especially important in order to avoid various emergency situations in networks. It is advisable to use machine learning methods to obtain information about signal quality, traffic, etc. At the same time it is possible to make forecasts of various malfunctions, routing, safety control.
It is determined that the model of Markov random field is effective in modeling inhomogeneous networks. This approach allows modeling the exponential distribution of nodes in heterogeneous networks.
A modification of the proximal gradient algorithm is presented — a method of variable metric proximal gradient. Ensuring fast convergence is achieved by means of diagonal step size, which is more efficient than scalar.
The article reveals an adaptive rule for choosing a metric, a diagonal step based on the Barzilai-Borvain (BB) method. The presented algorithm combines two approaches: the standard proximal gradient method and the proximal Newton method. The establishment of clear rules for choosing the diagonal step size for convex optimization algorithms has been implemented.
The proposed diagonal metric provides a better estimate of the ill-conditioned local Hessian compared to the standard Barzilai-Borwein BB scalar step, leading to faster convergence of the algorithm. Combined with non-monotonic linear search, the general algorithm is guaranteed to converge. Finally, for several machine learning programs with artificial and real datasets, empirical results demonstrate better convergence behavior for the proposed methodology.
Implementation of the proposed metric proximal gradient technique in the management of a heterogeneous telecommunication network will ensure effective decentralized management of heterogeneous network resources and reduce the amount of service information in the network. This will avoid overloading the network in the event of emergency situations. However, the question of the load on the network equipment during its management in the presence of a large number of users still remains open.

Keywords: convex optimization; optimization methods; machine learning; diagonal step size; Barzilai-Borvain method; proximal gradient.

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