Let Φ0 : Rn → R ∪ {+∞} be a closed convex function and Φ1 : Rn → R be a finite convex function that are bounded from below. Our goal is to build an algorithm which first minimizes the map Φ0 and… (More)

We investigate the asymptotic properties as t → ∞ of the differential equation ẍ(t) + a(t)ẋ(t) +∇G(x(t)) = 0, t ≥ 0 where x(·) is R-valued, the map a : R+ → R+ is non increasing, and G : R → R is a… (More)

Given a Hilbert space H and a function Φ : H → R of class C1, we investigate the asymptotic behavior of the trajectories associated to the following dynamical system (S) ẋ(t) + 1 k(t) ∫ t t0… (More)

Given γ ≥ 0, let us consider the following differential inclusion (S) ẍ(t) + γ ẋ(t) + ∂Φ(x(t)) 3 0, t ∈ R+, where Φ : Rd → R ∪ {+∞} is a lower semicontinuous convex function such that int(domΦ) 6= ∅.… (More)

We investigate the dynamics of an oscillator subject to dry friction via the following differential inclusion (S) ẍ(t) + ∂Φ(ẋ(t)) + ∇f(x(t)) 3 0, t ≥ 0, where f : R → R is a smooth potential and Φ :… (More)

Let Φ : H → R be a C function on a real Hilbert space and Σ ⊂ H × R the manifold defined by Σ := Graph (Φ). We study the motion of a material point with unit mass, subjected to stay on Σ and which… (More)

We investigate the asymptotic properties as t → ∞ of the following differential equation in the Hilbert space H (S) ẍ(t) + a(t)ẋ(t) +∇G(x(t)) = 0, t ≥ 0, where the map a : R+ → R+ is non increasing… (More)