Gradient projection method for convex function and strongly convex set**Supported by the Russian Foundation for Basic Research, grant 13-01-00295.

Golubev, Maxim O.

doi:10.1016/j.ifacol.2015.11.085

Cited by 4 publications

(1 citation statement)

References 2 publications

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“…To solve this problem, its discrete approximation can be applied using explicit difference schemes and numerical trajectories can be constructed [11].…”

Section: Resultsmentioning

confidence: 99%

Optimal cybersecurity management of an IP video surveillance system using neural network technologies

Tsarkova

2023

E3S Web of Conf.

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The aim of the study is to solve the actual problem of constructing an optimal strategy for managing a system for protecting against the spread of computer epidemics of IP video surveillance networks used in the work of distributed situational centers. The paper presents a new mathematical modeling apparatus for building an adaptive network protection system from cyber-attacks using a hybrid approach that uses both classical control and neurocontrol based on an artificial neural network.

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“…To solve this problem, its discrete approximation can be applied using explicit difference schemes and numerical trajectories can be constructed [11].…”

Section: Resultsmentioning

confidence: 99%

Optimal cybersecurity management of an IP video surveillance system using neural network technologies

Tsarkova

2023

E3S Web of Conf.

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Local Strong Convexity in Hilbert Space

Golubev

2020

Communications in Computer and Information Science

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Gradient Methods on Strongly Convex Feasible Sets and Optimal Control of Affine Systems

Veliov

Vuong

2018

Appl Math Optim

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The paper presents new results about convergence of the gradient projection and the conditional gradient methods for abstract minimization problems on strongly convex sets. In particular, linear convergence is proved, although the objective functional does not need to be convex. Such problems arise, in particular, when a recently developed discretization technique is applied to optimal control problems which are affine with respect to the control. This discretization technique has the advantage to provide higher accuracy of discretization (compared with the known discretization schemes) and involves strongly convex constraints and possibly non-convex objective functional. The applicability of the abstract results is proved in the case of linear-quadratic affine optimal control problems. A numerical example is given, confirming the theoretical findings. Keywords Optimal control • Mathematical programming • Numerical methods • Gradient methods • Affine control systems • Bang-bang control Mathematics Subject Classification 49M25 • 90C25 • 90C48 • 49M37

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Gradient projection method for convex function and strongly convex set**Supported by the Russian Foundation for Basic Research, grant 13-01-00295.

Cited by 4 publications

References 2 publications

Optimal cybersecurity management of an IP video surveillance system using neural network technologies

Optimal cybersecurity management of an IP video surveillance system using neural network technologies

Local Strong Convexity in Hilbert Space

Gradient Methods on Strongly Convex Feasible Sets and Optimal Control of Affine Systems

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