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Tytuł:
Error estimates for finite element approximations of elliptic control problems
Autorzy:
Alt, Walter
Bräutigam, Nils
Rösch, Arnd
Powiązania:
https://bibliotekanauki.pl/articles/729441.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Linear quadratic optimal control problems
elliptic equations
finite element approximations
error estimates
Opis:
We investigate finite element approximations of one-dimensional elliptic control problems. For semidiscretizations and full discretizations with piecewise constant controls we derive error estimates in the maximum norm.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 1; 7-22
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Collocation methods for the solution of eigenvalue problems for singular ordinary differential equations
Autorzy:
Auzinger, W.
Karner, E.
Koch, O.
Weinmuller, E.
Powiązania:
https://bibliotekanauki.pl/articles/255635.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
polynomial collocation
singular boundary value problems
linear and nonlinear eigenvalue problems
Opis:
We demonstrate that eigenvalue problems for ordinary differential equations can be recast in a formulation suitable for the solution by polynomial collocation. It is shown that the well-posedness of the two formulations is equivalent in the regular as well as in the singular case. Thus, a collocation code equipped with asymptotically correct error estimation and adaptive mesh selection can be successfully applied to compute the eigenvalues and eigenfunctions efficiently and with reliable control of the accuracy. Numerical examples illustrate this claim.
Źródło:
Opuscula Mathematica; 2006, 26, 2; 229-241
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal control of a two-dimensional linear system with a quadratic performance index with constraints on the trajectory and the control
Autorzy:
Biły, Barbara
Powiązania:
https://bibliotekanauki.pl/articles/747527.pdf
Data publikacji:
1997
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Linear-quadratic problems
Other methods
Opis:
.
The main purpose of this note is to present a method for solving the linear-quadratic optimal regulator for discrete, linear general two-dimensional system with constant coefficients. The quadratic optimal regulator problem can be formulated: find of sequence of control vectors in fixed rectangle, which transfer the system to given final state vector and minimizes the quadratic performance index, with constraints of control and state vector. This problem, by transformation for systemand performance index is reduced to equivalent mathematical programming problem. Necessary and sufficient conditions are established for the existence of a solution to this problem. With slight modifications the considerations can be extended for 2-D systems with variable coefficient and n-D linear systems.
Źródło:
Mathematica Applicanda; 1997, 26, 40
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
New efficient time integrators for non-linear parabolic problems
Autorzy:
Bujanda, B.
Jorge, J. C.
Powiązania:
https://bibliotekanauki.pl/articles/255918.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
fractional step methods
non-linear parabolic problems
convergence
Opis:
In this work a new numerical method is constructed for time-integrating multidimensional parabolic semilinear problems in a very efficient way. The method reaches the fourth order in time and it can be combined with standard spatial discretizations of any order to obtain unconditionally convergent numerical algorithms. The main theoretical results which guarantee this property are explained here, as well as the method characteristics which guarantee a very strong reduction of computational cost in comparison with classical discretization methods.
Źródło:
Opuscula Mathematica; 2006, 26, 3; 407-419
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Determination of Approaches for Project Costs Minimization with Use of Dual Problems
Autorzy:
Chernov, S.
Titov, S.
Chernova, L.
Kunanets, N.
Powiązania:
https://bibliotekanauki.pl/articles/410624.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Oddział w Lublinie PAN
Tematy:
linear optimization
primal problem
dual problem
duality
objective function
constraint system
pairs of dual problems
Opis:
For determining ways of company development, ensuring the growth of profit in manufacture and sales of certain products, it has been proposed to use an algorithm of constructing a problem being inverse to primal-dual one, for minimization of the project costs. The primal and the inverse problems contribute to improving the efficiency of calculation when determining approaches for minimization of costs. This pair of problems is mutually conjugate. The proposed rigorous approach to obtaining the algorithm of constructing a dual problem is based on the following statement: a problem being inverse to a dual one is a primal (original) problem. The authors have proposed and rigorously proven the algorithm of a general approach to the construction of conjugate problem pairs. Formalization of the algorithm developed allows obtaining easily correct pairs of known dual problems. This permitted proposing and proving the truth of the algorithm of constructing a dual problem for the arbitrary form of a primal problem representation.
Źródło:
ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes; 2019, 8, 2; 61-68
2084-5715
Pojawia się w:
ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal control for a nonstationary linear system with a quadratic cost functional
Autorzy:
Czornik, Adam
Powiązania:
https://bibliotekanauki.pl/articles/747535.pdf
Data publikacji:
1997
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Optimal stochastic control
Problems involving randomness
Linear-quadratic problems
Opis:
.
This paper is about optimal control of infinite-horizon nonstationary stochastic linear processes with a quadratic cost criterion. The synthesis problem of optimal control is solved under the assumptions that the criterion is an average expected cost and that the process' matrices possess limits for the time approaching infinity. Furthermore, the limit matrices are such that the "limit" process is both observable and controllable. The paper documents existence of an optimal feedback control policy. The policy is such that the gain matrix is a (scaled) solution to a Riccati stationary matrix equation. The equation is stationary in that its coefficients are the limits of the process' non-stationary matrices.
Źródło:
Mathematica Applicanda; 1997, 26, 40
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Regularity and existence of solutions to parabolic equations with nonstandard p(x,t),q(x,t)-growth conditions
Autorzy:
El Bahja, Hamid
Powiązania:
https://bibliotekanauki.pl/articles/29519471.pdf
Data publikacji:
2023
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
existence theory
non-linear parabolic problems
non-standard growth
regularity theory
Opis:
We study the Cauchy–Dirichlet problem for a class of nonlinear parabolic equations driven by nonstandard p(x, t), q(x, t)-growth condition. We prove theorems of existence and uniqueness of weak solutions in suitable Orlicz-Sobolev spaces, derive global and local in time $ L^\infty $ bounds for the weak solutions.
Źródło:
Opuscula Mathematica; 2023, 43, 6; 759-788
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An algorithm for the solution of the traveling salesman problem via disjunctive graphs
Autorzy:
Grabowski, Józef
Powiązania:
https://bibliotekanauki.pl/articles/748529.pdf
Data publikacji:
1978
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Directed graphs (digraphs), tournaments
Scheduling theory, deterministic
Special problems of linear programming(transportation, multi-index, etc.)
Opis:
.
From the introduction: "The traveling salesman problem is a problem of combinatorial type. Although problems of this type sometimes have a relatively simple formulation, there are many difficulties associated with their solution even when the most up-to-date computers are used. In the 1970s many papers have been devoted to this problem. The purpose of the vast majority of them has been to find more effective solution algorithms. "In this paper we give the solution of the traveling salesman problem via disjunctive graphs. Up to now the elements of disjunctive graphs have been used to solve problems connected with the determination of an optimal task completion sequence.''
Źródło:
Mathematica Applicanda; 1978, 6, 13
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fractional problems with right-handed Riemann-Lioville fractional derivatives
Autorzy:
Jankowski, T.
Powiązania:
https://bibliotekanauki.pl/articles/1938600.pdf
Data publikacji:
2016
Wydawca:
Politechnika Gdańska
Tematy:
right-handed Riemann-Liouville fractional derivatives
nonlinear boundary problems
linear problems
existence of solutions
Mittag-Leffler functions
Opis:
In this paper, we investigate the existence of solutions for advanced fractional differential equations containing the right-handed Riemann-Liouville fractional derivative both with nonlinear boundary conditions and also with initial conditions given at the end point T of interval [0,T]. We use both the method of successive approximations, the Banach fixed point theorem and the monotone iterative technique, as well. Linear problems are also discussed. A few examples illustrate the results.
Źródło:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2016, 20, 1; 63-83
1428-6394
Pojawia się w:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Gradient method for non-injective operators in Hilbert space with application to Neumann problems
Autorzy:
Karátson, János
Powiązania:
https://bibliotekanauki.pl/articles/1338793.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Neumann boundary value problems
non-injective non-linear operator
gradient method
Hilbert space
Opis:
The gradient method is developed for non-injective non-linear operators in Hilbert space that satisfy a translation invariance condition. The focus is on a class of non-differentiable operators. Linear convergence in norm is obtained. The method can be applied to quasilinear elliptic boundary value problems with Neumann boundary conditions.
Źródło:
Applicationes Mathematicae; 1999, 26, 3; 333-346
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Comparative Study of AMPL, Pyomo and JuMP Optimization Modeling Languages on a Network Linear Programming Problem Example
Studium porównawcze języków modelowania optymalizacyjnego AMPL, Pyomo i JuMP na przykładzie liniowego zadania programowania sieciowego
Autorzy:
Karbowski, Andrzej
Wyskiel, Krzysztof
Powiązania:
https://bibliotekanauki.pl/articles/2068625.pdf
Data publikacji:
2021
Wydawca:
Sieć Badawcza Łukasiewicz - Przemysłowy Instytut Automatyki i Pomiarów
Tematy:
optimization
modeling languages
programming
shortest path problem
network problems
linear programming
optymalizacja
języki modelowania
zadanie najkrótszej ścieżki
zadania sieciowe
programowanie liniowe
zadania grafowe
Opis:
The purpose of this work is a comparative study of three languages (environments) of optimization modeling: AMPL, Pyomo and JuMP. The comparison will be based on three implementations of the shortest path problem formulated as a linear programming problem. The codes for individual models and differences between them will be presented and discussed. Various aspects will be taken into account, such as: simplicity and intuitiveness of implementation, availability of specific data structures for a LP network problems, etc.
Celem pracy jest zbadanie i porównanie możliwości trzech języków (środowisk) modelowania optymalizacyjnego: AMPL, Pyomo i JuMP. Porównanie zostanie oparte na trzech implementacjach zadania najkrótszej ścieżki sformułowanego jako zadanie programowania liniowego. Przedstawione i omówione zostaną kody poszczególnych modeli oraz różnice między nimi. Pod uwagę będą brane różne aspekty, takie jak: prostota i intuicyjność implementacji, dostępność określonych struktur danych dla problemów z siecią LP itp.
Źródło:
Pomiary Automatyka Robotyka; 2021, 25, 3; 23--30
1427-9126
Pojawia się w:
Pomiary Automatyka Robotyka
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solving of linear programming by method of structural optimization
Autorzy:
Karganov, S. A.
Powiązania:
https://bibliotekanauki.pl/articles/906235.pdf
Data publikacji:
2013
Wydawca:
Akademia Morska w Szczecinie. Wydawnictwo AMSz
Tematy:
linear programming
direct and inverse problems
simplex method
objectively determined valuations
structural optimization
Opis:
The paper lists the problems hindering the use in business practices of the results of solving direct and inverse problems in linear programming. It is shown that overcoming these obstacles lies in the way of using of developed by the author and described in this paper method of structural optimization and algorithms for its implementation. Here are some examples of solutions by the method of structural optimization of production planning problems.
Źródło:
Zeszyty Naukowe Akademii Morskiej w Szczecinie; 2013, 34 (106); 48-58
1733-8670
2392-0378
Pojawia się w:
Zeszyty Naukowe Akademii Morskiej w Szczecinie
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
ADI-based, conditionally stable schemes for seismic P-wave and elastic wave propagation problems
Autorzy:
Łoś, Marcin
Behnoudfar, Pouria
Dobija, Mateusz
Paszyński, Maciej
Powiązania:
https://bibliotekanauki.pl/articles/2173701.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
conditional stability
P-wave propagation problems
elastic wave propagation problems
linear computational cost
time-dependent simulations
stabilność warunkowa
problemy z propagacją fali P
problemy z propagacją fali sprężystej
koszt obliczeniowy liniowy
symulacje zależne od czasu
Opis:
The modeling of P-waves has essential applications in seismology. This is because the detection of the P-waves is the first warning sign of the incoming earthquake. Thus, P-wave detection is an important part of an earthquake monitoring system. In this paper, we introduce a linear computational cost simulator for three-dimensional simulations of P-waves. We also generalize our formulations and derivation for elastic wave propagation problems. We use the alternating direction method with isogeometric finite elements to simulate seismic P-wave and elastic propagation problems. We introduce intermediate time steps and separate our differential operator into a summation of the blocks, acting along the particular coordinate axis in the sub-steps. We show that the resulting problem matrix can be represented as a multiplication of three multi-diagonal matrices, each one with B-spline basis functions along the particular axis of the spatial system of coordinates. The resulting system of linear equations can be factorized in linear O (N) computational cost in every time step of the semi-implicit method. We use our method to simulate P-wave and elastic wave propagation problems. We derive the condition for the stability for seismic waves; namely, we show that the method is stable when τ < C min{ hx,hy,hz}, where C is a constant that depends on the PDE problem and also on the degree of splines used for the spatial approximation. We conclude our presentation with numerical results for seismic P-wave and elastic wave propagation problems.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2022, 70, 5; art. no. e141985
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Finite element error analysis for state-constrained optimal control of the Stokes equations
Autorzy:
Los Reyes, J. C. de
Meyer, C.
Vexler, B.
Powiązania:
https://bibliotekanauki.pl/articles/969607.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
równanie Stokesa
aproksymacja numeryczna
element skończony
linear quadratic optimal control problems
Stokes equations
state constraints
numerical approximation
finite elements
Opis:
An optimal control problem for 2d and 3d Stokes equations is investigated with pointwise inequality constraints on the state and the control. The paper is concerned with the full discretization of the control problem allowing for different types of discretization of both the control and the state. For instance, piecewise linear and continuous approximations of the control are included in the present theory. Under certain assumptions on the L∞-error of the finite element discretization of the state, error estimates for the control are derived which can be seen to be optimal since their order of convergence coincides with the one of the interpolation error. The assumptions of the L∞-finite-eleinent-error can be verified for different numerical settings. Finally the results of two numerical experiments are presented.
Źródło:
Control and Cybernetics; 2008, 37, 2; 251-284
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Boundary-Value Problem for Linear Pdaes
Autorzy:
Marszałek, W.
Trzaska, Z.
Powiązania:
https://bibliotekanauki.pl/articles/908511.pdf
Data publikacji:
2002
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
matematyka
differential algebraic equations
boundary value problems
linear multivariable systems
Opis:
We analyze a boundary-value problem for linear partial differential algebraic equations, or PDAEs, by using the method of the separation of variables. The analysis is based on the Kronecker-Weierstrass form of the matrix pencil [A,-ln B]. A new theorem is proved and two illustrative examples are given.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2002, 12, 4; 487-491
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 30

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