Temat: monotone methods - Prolib Integro

Skocz do pozycji: 1.

Tytuł:: On unique solvability of a Dirichlet problem with nonlinearity depending on the derivative
Autorzy:: Bełdziński, Michał
Galewski, Marek
Tematy:: diffeomorphism
uniqueness non-potential problems
variational methods
monotone methods
Palais-Smale condition; Pokaż więcej
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Powiązania:: https://bibliotekanauki.pl/articles/256038.pdf Link otwiera się w nowym oknie
Opis:: In this work we consider second order Dirichelet boundary value problem with nonlinearity depending on the derivative. Using a global diffeomorphism theorem we propose a new variational approach leading to the existence and uniqueness result for such problems.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Signal reconstruction from given phase of the Fourier transform using Fejér monotone methods
Autorzy:: Schott, Dieter
Tematy:: signal reconstruction
convex feasibility problem
projection onto convex sets
Fejér monotone iterative methods
Fourier transforms; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/729265.pdf Link otwiera się w nowym oknie
Opis:: The aim is to reconstruct a signal function x ∈ L₂ if the phase of the Fourier transform [x̂] and some additional a-priori information of convex type are known. The problem can be described as a convex feasibility problem. We solve this problem by different Fejér monotone iterative methods comparing the results and discussing the choice of relaxation parameters. Since the a-priori information is partly related to the spectral space the Fourier transform and its inverse have to be applied in each iterative step numerically realized by FFT techniques. The computation uses MATLAB routines.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: Monotone iterative methods for infinite systems of reaction-diffusion-convection equations with functional dependence
Autorzy:: Brzychczy, S.
Tematy:: infinite systems
reaction-diffusion-convection equations
semilinear parabolic differential-functional equations
Volterra functionals
monotone iterative methods
method of upper and lower solutions; Pokaż więcej
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Powiązania:: https://bibliotekanauki.pl/articles/255097.pdf Link otwiera się w nowym oknie
Opis:: We consider the Fourier first initial-boundary value problem for an infinite system of semilinear parabolic differential-functional equations of reaction-diffusion-convection type of the form [formula] where [formula] in a bounded cylindrical domain (0, T] x G := D rcup Rm+1. The right-hand sides of the system are Volterra type functionals of the unknown function z. In the paper, we give methods of the construction of the monotone iterative sequences converging to the unique classical solution of the problem considered in partially ordered Banach spaces with various convergence rates of iterations. We also give remarks on monotone iterative methods in connection with numerical methods, remarks on methods for the construction of lower and upper solutions and remarks concerning the possibility of extending these methods to more general parabolic equations. All monotone iterative methods are based on differential inequalities and, in this paper, we use the theorem on weak partial differential-functional inequalities for infinite systems of parabolic equations, the comparison theorem and the maximum principle. A part of the paper is based on the results of our previous papers. These results generalize the results obtained by several authors in numerous papers for finite systems of semilinear parabolic differential equations to encompass the case of infinite systems of semilinear parabolic differential-functional equations. The monotone iterative schemes can be used for the computation of numerical solutions.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: On convergence of the Monotone Structural Evolution
Autorzy:: Korytowski, A.
Szymkat, M.
Tematy:: optimal control
direct computational methods
gradient optimization
monotone structural evolution; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Powiązania:: https://bibliotekanauki.pl/articles/206572.pdf Link otwiera się w nowym oknie
Opis:: The paper studies convergenceof the Monotone Structural Evolution (MSE), a computational method of optimal control. The principles of MSE are described and an expository example presents the method in action. It is then proved that under appropriate assumptions the method is convergent to the decision space stationarity conditions. Observations on ﬁnite convergence and on connections with Pontryagin’s maximum principle are also provided.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 5.

Tytuł:: Proximal-based regularization methods and successive approximation of variational inequalities in Hilbert spaces
Autorzy:: Kaplan, A.
Tichatschke, R.
Tematy:: funkcja Bregmana
metoda punktów proksymalnych
nierówność wariacyjna
operator monotoniczny
regularyzacja
Bregman function
monotone operators
proximal point methods
regularization
variational inequalities; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Powiązania:: https://bibliotekanauki.pl/articles/205832.pdf Link otwiera się w nowym oknie
Opis:: For variational inequalities with multi-valued, maximal monotone operators in Hilbert spaces we study proximal-based methods with an improvement of the data approximation after each (approximately performed) proximal iteration. The standard conditions on a distance functional of Bregman's type are weakened, depending on a "reserve of monotonicity" of the operator in the variational inequality, and the enlargement concept is used for approximating the operator. Weak convergence of the proxinnal iterates to a solution of tire original problem is proved. The construction of the [epsilon]-enlargement of monotone operators is analyzed for some particular cases.
Dostawca treści:: Biblioteka Nauki

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