Optimizing properties of an inertial dynamical system with geometric damping : link with proximal methods

• Autorzy: Attouch H. , Bolte J. , Redont P.
• Języki publikacji: EN

Abstrakty

EN

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].

Słowa kluczowe

EN

dynamical systems in optimization; entropic methods in optimization; proximal regularization method; steepest descent method

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2002
• Tom: Vol. 31, no 3
• Strony: 643--657
• Opis fizyczny: Bibliogr. 24 poz.,

Twórcy

autor

Attouch H.

autor

Bolte J.

autor

Redont P.