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Wyszukujesz frazę "Osmolovskii, Nikolai P." wg kryterium: Autor


Wyświetlanie 1-3 z 3
Tytuł:
A second-order sufficient condition for a weak local minimum in an optimal control problem with an inequality control constraint
Autorzy:
Osmolovskii, Nikolai P.
Powiązania:
https://bibliotekanauki.pl/articles/2183496.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
critical cone
quadratic form
first order tangent
second order tangent
second order optimality conditions
weak local minimum
inequality control constraint
Pontryagin’s maximum principle
Opis:
This paper is devoted to a sufficient second-order condition for a weak local minimum in a simple optimal control problem with one control constraint G(u) ≤ 0, given by a C2-function. A similar second-order condition was obtained earlier by the author for a strong minimum in a much more general problem. In the present paper, we would like to take a narrower perspective than before and thus provide shorter and simpler proofs. In addition, the paper uses the first and second order tangents to the set U, defined by the inequality G(u) ≤ 0. The main difficulty of the proof, clearly shown in the paper, refers to the set, where the gradient Hu of the Hamiltonian is small, but the condition of quadratic growth of the Hamiltonian is satisfied. The paper can be valuable for self-explanation and provides a basis for extensions.
Źródło:
Control and Cybernetics; 2022, 51, 2; 151--169
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Network optimality conditions
Autorzy:
Osmolovskii, Nikolai P.
Qian, Meizhi
Sokołowski, Jan
Powiązania:
https://bibliotekanauki.pl/articles/31343935.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
network
optimal control problem
weak local minimum
Pontryagin’s maximum principle
critical cone
quadratic form
second order optimality conditions
Riccati equation
Opis:
Optimality conditions for optimal control problems arising in network modeling are discussed. We confine ourselves to the steady state network models. Therefore, we consider only control systems described by ordinary differential equations. First, we derive optimality conditions for the nonlinear problem for a single beam. These conditions are formulated in terms of the local Pontryagin maximum principle and the matrix Riccati equation. Then, the optimality conditions for the control problem for networks posed on an arbitrary planar graph are discussed. This problem has a set of independent variables xi varying within their intervals [0, li], associated with the corresponding beams at network edges. The lengths li of intervals are not specified and must be determined. So, the optimization problem is non-standard, it is a combination of control and design of networks. However, using a linear change of the independent variables, it can be reduced to a standard one, and we show this. Two simple numerical examples for the single-beam problem are considered.
Źródło:
Control and Cybernetics; 2023, 52, 2; 129-180
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the strong metric subregularity in mathematical programming
Autorzy:
Osmolovskii, Nikolai P.
Veliov, Vladimir M.
Powiązania:
https://bibliotekanauki.pl/articles/2183475.pdf
Data publikacji:
2021
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimization
mathematical programming
Karush-Kuhn-Tucker conditions
metric regularity
Opis:
This note presents sufficient conditions for the property of strong metric subregularity (SMSr) of the system of first order optimality conditions for a mathematical programming problem in a Banach space (the Karush-Kuhn-Tucker conditions). The constraints of the problem consist of equations in a Banach space setting and a finite number of inequalities. The conditions, under which SMSr is proven, assume that the data are twice continuously Fréchet differentiable, the strict Mangasarian-Fromovitz constraint qualification is satisfied, and the second-order sufficient optimality condition holds. The obtained result extends the one known for finite-dimensional problems. Although the applicability of the result is limited to the Banach space setting (due to the twice Fréchet differentiability assumptions and the finite number of inequality constraints), the paper can be valuable due to the self-contained exposition, and provides a ground for extensions. One possible extension was recently implemented in Osmolovskii and Veliov (2021).
Źródło:
Control and Cybernetics; 2021, 50, 4; 457--471
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
    Wyświetlanie 1-3 z 3

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