- Tytuł:
- Optimizing properties of an inertial dynamical system with geometric damping : link with proximal methods
- Autorzy:
-
Attouch, H.
Bolte, J.
Redont, P. - Powiązania:
- https://bibliotekanauki.pl/articles/205719.pdf
- Data publikacji:
- 2002
- Wydawca:
- Polska Akademia Nauk. Instytut Badań Systemowych PAN
- Tematy:
-
dynamical systems in optimization
entropic methods in optimization
proximal regularization method
steepest descent method - 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].
- Źródło:
-
Control and Cybernetics; 2002, 31, 3; 643-657
0324-8569 - Pojawia się w:
- Control and Cybernetics
- Dostawca treści:
- Biblioteka Nauki
Artykuł