Inexact Proximal Algorithm for Nonlinear Optimization
par
Isai Lankoande(Université de Limoges)
→
Europe/Paris
XLIM Salle X.203
XLIM Salle X.203
FST-Université de Limoges,
123, Av. Albert Thomas.
Description
In this talk, we describe an inexact proximal regularization algorithm
for solving a smooth unconstrained minimization problem. We consider
the minimization problem
\min_{x \in \mathbb{R}^n} f(x),
where $f : \mathbb{R}^n \longrightarrow \mathbb{R}$ is a smooth
function. Starting from an initial point $x_0 \in \mathbb{R}^n$, at
iteration $k \in \mathbb{N}$, a solution $x_{k+1}$ is computed by
approximately solving the problem
\min_{x \in \mathbb{R}^n}\varphi_k(x) := f(x) + \frac{\theta_k}{2}\|x
- x_k\|^2
where $\theta_k > 0$ is a given parameter. We present the algorithm
and compare it with the existing algorithms. We present also some
convergence results and numerical experiments.
