Temat: steepest descent method

Skocz do pozycji: 1.

Tytuł:: Optimizing properties of an inertial dynamical system with geometric damping : link with proximal methods
Autorzy:: Attouch, H.
Bolte, J.
Redont, P.
Tematy:: dynamical systems in optimization
entropic methods in optimization
proximal regularization method
steepest descent method; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Powiązania:: https://bibliotekanauki.pl/articles/205719.pdf Link otwiera się w nowym oknie
Opis:: The second-order dynamical system x + [alpha]x + Beta[...] = 0, alpha > 0, Beta > 0, where the Hessian [...]Phi(x) acts as a geometric damping, is introduced, mainly in view of the minimization of [Phi]. Minimizing [Phi] is a problem equivalent to the minimization of the functional [Psi]a,b(x, y) = 1/b^2Phi(x) + 1/2|ax + by|^2, a > 0, b > 0. The latter naturallv appears in the proximal regularization of Phi ; it may also be viewed as an energy. The continuous steepest descent method applied to [Psi]a,b yields a first-order system, which proves to he equivalent to the above-mentioned second-order system, when [Phi] is of class [C^2].
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Optymalna dywersyfikacja portfela akcji metodami gradientowymi przy użyciu algorytmów numerycznych
Optimal portfolio diversification by gradient-based numerical algorithms
Autorzy:: Olbryś, Patrycja
Opis:: Tematem pracy jest rozwiązywanie zadań optymalizacji nieliniowej przy użyciu metod gradientowych z zastosowaniem algorytmów numerycznych. W pracy zostały scharakteryzowane dwie metody: metoda najszybszego spadku oraz metoda gradientu sprzężonego. Zastosowano je do rozwiązania problemu maksymalizacji współczynnika dywersyfikacji portfela akcji.
The subject of the thesis is solving nonlinear optimization problems by using gradient numerical methods. There are presented two methods: the steepest descent method and the conjugate gradient method. The algorithms are applied to solve the problem of maximization of portfolio diversification ratio.
Dostawca treści:: Repozytorium Uniwersytetu Jagiellońskiego

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Skocz do pozycji: 3.

Tytuł:: Internal wave diffraction by a strip of an elastic plate on the surface of a stratified fluid
Autorzy:: Dolai, P.
Dolai, D. P.
Tematy:: równanie Kleina-Gordona
płyn warstwowy
metoda Wienera-Hopfa
stratified fluid
Klein-Gordon equation
Wiener-Hopf technique
steepest descent method; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Oficyna Wydawnicza
Powiązania:: https://bibliotekanauki.pl/articles/265771.pdf Link otwiera się w nowym oknie
Opis:: The problem of internal wave diffraction by a strip of an elastic plate of finite width present on the surface of an exponentially stratified liquid is investigated in this paper. Assuming linear theory, the problem is formulated in terms of a function related to the stream function describing the motion in the liquid. The related boundary value problem involves a hyperbolic type partial differential equation (PDE), known as the Klein Gordon equation. The method of Wiener-Hopf is utilized in the mathematical analysis to a slightly generalized boundary value problem (BVP) by introducing a small parameter, and the problem is solved approximately for large width of the plate. In the final results, this small parameter is made to tend to zero. The diffracted field is obtained in terms of integrals, which are then evaluated asymptotically in different regions for a large distance from the edges of the plate and the results are interpreted physically.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: Hand drill shape optimization using Open CASCADE library and the steepest descent method
Autorzy:: Król, Roman
Tematy:: hand drills
drill bits
milling
finite element analysis
structural optimization
Open
CASCADE
steepest descent method
wiertarka ręczna
wiertło
frezowanie
analiza elementów skończonych
optymalizacja strukturalna; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Czasopisma i Monografie PAN
Powiązania:: https://bibliotekanauki.pl/articles/59498599.pdf Link otwiera się w nowym oknie
Opis:: In this article, compliance optimization with the steepest descent method of the hand drill bits shapes for metal drilling is presented. The analysis of stress, displacements and compliance of the solid with random shape can be performed using the finite element method. In the case of a high number of optimization iterations, each analysis needs automatic modifications of geometry, mesh and boundary conditions. The Open CASCADE library can be used in the fast and automatic construction of modified models. It allows for fast reanalysis for each derivative of the objective function in the optimization process. The motivation of this research is to fill the gap in the literature on drilling technology. Most of the contemporary research is devoted to the oil and gas industry, while optimization of the hand drill bits used in metal drilling is rare. Compliance optimization allows us to find the shape which guarantees a greater stiffness for the specified loading conditions and a given amount of material. Although the obtained compliance was low, further experimental research would be needed to apply new solutions in drilling practice. This will involve the construction of the drill bit tips and the development of a heat treatment process.
Dostawca treści:: Biblioteka Nauki

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