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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:
A singular nonlinear boundary value problem with Neumann conditions
Autorzy:
Janus, J.
Powiązania:
https://bibliotekanauki.pl/articles/255233.pdf
Data publikacji:
2005
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
singular nonlinear boundary value problem
Neumann boundary conditions
second order equations
maximal and minimal solutions
Opis:
We study the existence of solutions for the equations x" plmin g(t, x) = h(t), t mem (0, 1) with Neumann boundary conditions, where g: [0, 1] x (0, +infin) arr [0, +infin] and h: [0, 1] arr R are continuous and g(t, ·) is singular at 0 for each t mem [0, 1].
Źródło:
Opuscula Mathematica; 2005, 25, 2; 227-241
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A study of MHD fluid with second order slip and thermal flow over a nonlinear stretching sheet
Autorzy:
Jauhri, Shefali
Mishra, Upendra
Powiązania:
https://bibliotekanauki.pl/articles/2174199.pdf
Data publikacji:
2022
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
płyn magnetyczny
nanociecz
metoda Runge-Kutty
stagnation point flow
second order slip boundary conditions
nonlinear stretching sheet
Runge-Kutta method
Opis:
An electrically conducted viscous incompressible nanofluid flow caused by the nonlinear stretching surface with stagnation flow has been investigated numerically. The effect of Brownian motion and thermophoresis on the nanofluid is also incorporated. The governing partial differential equations with nonlinear second order boundary conditions are solved by the fourth order Runge-Kutta technique using MATLAB programming. The effect of the radiation parameter (Rd), stretching parameter (n), Brownian motion parameter (Nb), thermophoresis parameter (Nt) on temperature, velocity and mass transfer are shown graphically. The influence of some of these parameters on the local Nusselt number (−′(0)) and local Sherwood number (−′(0)) are shown by the graphs.
Źródło:
International Journal of Applied Mechanics and Engineering; 2022, 27, 2; 98--114
1734-4492
2353-9003
Pojawia się w:
International Journal of Applied Mechanics and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Boundary integral representations of second derivatives in shape optimization
Autorzy:
Eppler, Karsten
Powiązania:
https://bibliotekanauki.pl/articles/729245.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
optimal shape design
fundamental solution
boundary integral equation
second-order derivatives
optimality conditions
Opis:
For a shape optimization problem second derivatives are investigated, obtained by a special approach for the description of the boundary variation and the use of a potential ansatz for the state. The natural embedding of the problem in a Banach space allows the application of a standard differential calculus in order to get second derivatives by a straight forward "repetition of differentiation". Moreover, by using boundary value characerizations for more regular data, a complete boundary integral representation of the second derivative of the objective is possible. Basing on this, one easily obtains that the second derivative contains only normal components for stationary domains, i.e. for domains, satisfying the first order necessary condition for a free optimum. Moreover, the nature of the second derivative is discussed, which is helpful for the investigation of sufficient optimality conditions.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2000, 20, 1; 63-78
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
C^11 vector optimization problems and Riemann derivatives
Autorzy:
Ginchev, I.
Guerraggio, A.
Rocca, M.
Powiązania:
https://bibliotekanauki.pl/articles/970359.pdf
Data publikacji:
2004
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optymalizacja wektorowa
pochodna kierunkowa typu Riemanna
warunek optymalności dwuwskaźnikowy
vector optimization
Riemann-type directional derivatives
second-order optimality conditions
Opis:
In this paper we introduce a generalized second-order Riemann-type derivative for C^1'1 vector functions and use it to establish necessary and sufficient optimality conditions for vector optimization problems. We show that, these conditions are stronger than those obtained by means of the second-order subdinerential in Clarke sense considered in Guerraggio, Luc (2001) and also to some extent than those obtained in Guerraggio, Luc, Minh (2001).
Źródło:
Control and Cybernetics; 2004, 33, 2; 259-273
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Equivalence of second order optimality conditions for bang-bang control problems. Part 1: Main results
Autorzy:
Osmolovskii, N. P.
Maurer, H.
Powiązania:
https://bibliotekanauki.pl/articles/970559.pdf
Data publikacji:
2005
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sterowanie przekaźnikowe
stożek krytyczny
forma kwadratowa i równoważność
bang-bang control
second order necessary and sufficient conditions
critical cone
Opis:
Second order optimality conditions have been derived in the literature in two different forms. Osmolovskii (1988a, 1995, 2000, 2004) obtained second order necessary and sufficient conditions requiring that, a certain quadratic form be positive (semi)-definite on a critical cone. Agrachev, Stefani, Zezza (2002) first, reduced the bang-bang control problem to finite-dimensional optimization and then show that well-known sufficient optimality conditions for this optimization problem supplemented by the strict bang-bang property furnish sufficient conditions for the bang-bang control problem. In this paper, we establish the equivalence of both forms of sufficient conditions and give explicit relations between corresponding Lagrange multipliers and elements of critical cones. Part 1 summarizes the main results while detailed proofs will be given in Part 2.
Źródło:
Control and Cybernetics; 2005, 34, 3; 927-950
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Equivalence of second order optimality conditions for bang-bang control problems. Part 2 : Proofs, variational derivatives and representations
Autorzy:
Osmolovskii, N. P.
Maurer, H.
Powiązania:
https://bibliotekanauki.pl/articles/969736.pdf
Data publikacji:
2007
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
bang-bang control
second order necessary and sufficient conditions
critical cones
equivalence of quadratic forms
representation of the Hessian of the Lagrangian
Opis:
In Part 1 of this paper (Osmolovskii and Maurer, 2005), we have summarized the main results on the equivalence of two quadratic forms from which second order necessary and sufficient conditions can be derived for optimal bang-bang control problems. Here, in Part 2, we give detailed proofs and elaborate explicit relations between Lagrange multipliers and elements of the critical cones in both approaches. The main analysis concerns the derivation of formulas for the first and second order derivatives of trajectories with respect to variations of switching times, initial and final time and initial point. This leads to explicit representations of the second order derivatives of the Lagrangian for the induced optimization problem. Based on a suitable transformation, we obtain the elements of the Hessian of the Lagrangian in a form which involves only first order variations of the nominal trajectory. Finally, a careful regrouping of all terms allows us to find the desired equivalence of the two quadratic forms.
Źródło:
Control and Cybernetics; 2007, 36, 1; 5-45
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Exact penalization of pointwise constraints for optimal control problems
Autorzy:
Casas, E.
Powiązania:
https://bibliotekanauki.pl/articles/970884.pdf
Data publikacji:
2009
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal control
semilinear elliptic equations
pointwise state constraints
exact penalization
first and second order optimality conditions
Opis:
In this paper we consider a control problem governed by a semilinear elliptic equation with pointwise control and state constraints. We analyze the existence of an exact penalization of the state constraints. In particular, we prove that the first and second order optimality conditions imply the existence of such a penalization. Finally, we prove some extra regularity of the strict local minima of the control problem, assuming the existence of an exact penalization for them.
Źródło:
Control and Cybernetics; 2009, 38, 4A; 1131-1150
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Extracting second-order structures from single-input state-space models: application to model order reduction
Autorzy:
Guillet, J.
Mourllion, B.
Birouche, A.
Basset, M.
Powiązania:
https://bibliotekanauki.pl/articles/907584.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
model drugiego rzędu
obcinanie zrównoważone
obcinanie modalne
second order form model
preservation of the structural conditions
balanced truncation
modal truncation
Opis:
This paper focuses on the model order reduction problem of second-order form models. The aim is to provide a reduction procedure which guarantees the preservation of the physical structural conditions of second-order form models. To solve this problem, a new approach has been developed to transform a second-order form model from a state-space realization which ensures the preservation of the structural conditions. This new approach is designed for controllable single-input state-space realizations with real matrices and has been applied to reduce a single-input second-order form model by balanced truncation and modal truncation.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2011, 21, 3; 509-519
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Extremals of the time optimal control problem for a material point moving along a straight line in the presence of friction and limitation on the velocity
Autorzy:
Osmolovskii, N. P.
Figura, A.
Kośka, M.
Wójtowicz, M.
Powiązania:
https://bibliotekanauki.pl/articles/206453.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
material point
resistance forces
acceleration
deceleration
Pontryagin’s maximum principle
second order optimality conditions
optimal control
adjoint variable
state constraint
Stieltjes measure
singular arc
boundary arc
Opis:
This paper provides an analysis of the time optimal control problem for a material point moving along a straight line in the presence of strength of resistance to movement (friction) and subject to constraint on the velocity. The point is controlled by a limited traction or braking force. The analysis of the problem is based on the maximum principle for state constraints in the Dubovitskii-Milyutin form, see Dubovitskii and Milyutin (1965), and the necessary second-order optimality condition for bang-bang controls, see Milyutin and Osmolovskii (1998).
Źródło:
Control and Cybernetics; 2017, 46, 4; 305-324
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Glosa do wyroku Sądu Najwyższego z dnia 5 marca 2014 r., sygn. IV KK 341/13
Autorzy:
Kruk, Ewa
Powiązania:
https://bibliotekanauki.pl/articles/1393263.pdf
Data publikacji:
2016-03-31
Wydawca:
Uczelnia Łazarskiego. Oficyna Wydawnicza
Tematy:
relation between the acts of ‘development’ and ‘issue’ of an order on presenting
charges
conditions under which an order on presenting charges may be considered issued
withdrawal from the announcement of an order on presenting charges and taking a decision to
attach it to the case files
relacja pomiędzy „sporządzeniem” a „wydaniem” postanowienia o przedstawieniu zarzutów
warunki uznania postanowienia o przedstawieniu zarzutów za wydane
odstąpienie od ogłoszenia postanowienia o przedstawieniu zarzutów i poprzestanie na załączeniu go
do akt sprawy
Opis:
Pogląd Sądu Najwyższego zasługuje na częściową aprobatę. Czynności polegające na „sporządzeniu” oraz „wydaniu” postanowienia o przedstawieniu zarzutów nie powinny być z sobą utożsamiane. Wspomniane postanowienie można bowiem uznać za wydane dopiero po jego ogłoszeniu (z wyjątkiem sytuacji wskazanych w przepisie art. 313 § 1 k.p.k. in fine). Niezwłoczne przystąpienie do przesłuchania podejrzanego, podobnie jak promulgacja wyżej wymienionej decyzji procesowej, jest zaś obowiązkiem organów ścigania, nie stanowi jednak warunku wydania prawnie skutecznego postanowienia o przedstawieniu zarzutów, które sprawia, iż postępowanie przygotowawcze przekształca się z fazy in rem w fazę in personam.
The opinion of the Supreme Court deserves partial approval. Acts of the ‘development’ and ‘issue’ of an order on presenting charges should not be equated with each other. The above-mentioned order may be considered issued only after its publication (with the exception of the situations laid down in Article 313 § 1 of the Criminal Procedure Code in fine). A suspect’s interrogation without delay as well as the promulgation of the above-mentioned procedural decision is a duty of the law enforcement agencies. However, it is not a necessary condition under which a legally effective order on presenting charges (which transforms the preparatory proceedings from the in rem phase into the in personam phase) can be issued.
Źródło:
Ius Novum; 2016, 10, 1; 174-177
1897-5577
Pojawia się w:
Ius Novum
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Graniczne dystrybuanty wartości ekstremalnych dla zależnych ciągów zmiennych losowych
Limiting distribution function of extreme values for the dependent sequences random variables
Autorzy:
Kuźmiński, Łukasz
Powiązania:
https://bibliotekanauki.pl/articles/425143.pdf
Data publikacji:
2013
Wydawca:
Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
Tematy:
order statistics
limiting distribution function of extreme
dependence conditions D(un) and D’(un)
extreme index
Opis:
In the article the outline of asymptotic theory of extreme values has been intro-duced for the application to finance, hydrology and insurance. The study includes the theo-rems and the definitions which give the possibility to appoint the limiting distribution func-tion for the distributions of maximum in three cases. The first case concerns the sequence independent random variables. The second case concerns the stationary processes of random variables for which the conditions D(un) and D’(un) are satisfied (i.e. “the extinguishing de-pendence”). The last case concerns the stationary processes for which the conditions D(un) and D’(un) are not satisfied.
Źródło:
Econometrics. Ekonometria. Advances in Applied Data Analytics; 2013, 2(40); 115-125
1507-3866
Pojawia się w:
Econometrics. Ekonometria. Advances in Applied Data Analytics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Higher-order conditions for local equilibria in a discontinuous Gale economic model
Autorzy:
Michalak, A.
Studniarski, M.
Powiązania:
https://bibliotekanauki.pl/articles/205957.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
Gale model
equilibrium
higher-order conditions
generalized directional derivatives
Opis:
The paper introduces the concept of a strict local equilibrium of order k in the Gale economic model. We obtain higher-order necessary and sufficient conditions for such equilibria without assuming continuity of the utility functions. These conditions are formulated in terms of generalized lower and upper directional derivatives, introduced by Studniarski (1986). A stability theorem for strict local equilibria of order k is also included.
Źródło:
Control and Cybernetics; 2017, 46, 1; 37-47
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Lipschitz stability of optimal controls for the steady-state Navier-Stokes equations
Autorzy:
Roubicek, T.
Troltzsch, F.
Powiązania:
https://bibliotekanauki.pl/articles/970527.pdf
Data publikacji:
2003
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sterowanie strumieniem danych
stabilność Lipschitza
incompressible viscous fluids
flow control
first and second order optimality conditions
Lipschitz stability
Opis:
An optimal control problem with quadratic cost functional for the steady-state Navier-Stokes equations with no-slip boundary condition is considered. Lipschitz stability of locally optimal controls with respect to certain perturbations of both the cost functional and the equation is proved provided a second-order sufficient optimality condition holds. For a sufficiently small Reynolds number, even global Lipschitz stability of the unique optimal control is shown.
Źródło:
Control and Cybernetics; 2003, 32, 3; 683-705
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Local error structures and order conditions in terms of Lie elements for exponential splitting schemes
Autorzy:
Auzinger, W.
Herfort, W.
Powiązania:
https://bibliotekanauki.pl/articles/255869.pdf
Data publikacji:
2014
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
exponential splitting schemes
local error
defect
order conditions
free Lie algebra
Opis:
We discuss the structure of the local error of exponential operator splitting methods. In particular, it is shown that the leading error term is a Lie element, i.e., a linear combination of higher-degree commutators of the given operators. This structural assertion can be used to formulate a simple algorithm for the automatic generation of a minimal set of polynomial equations representing the order conditions, for the general case as well as in symmetric settings.
Źródło:
Opuscula Mathematica; 2014, 34, 2; 243-256
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 37

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