Inexact Proximal Algorithm for Nonlinear Optimization

par Isai Lankoande (Université de Limoges)

vendredi 20 mars 2015, 10:30 → 11:30 Europe/Paris

XLIM Salle X.203

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 $f:{\mathbb{R}}^n⟶\mathbb{R}$ 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.