Nondifferentiable Augmented Lagrangian, $\epsilon$-Proximal penalty methods and Applications

Noureddine. Dailia,*  and K. Saadib

Nondifferentiable Augmented Lagrangian, $\epsilon$-Proximal penalty methods and Applications

Authors :

Noureddine. Daili^a,* and K. Saadi^b

Author Address :

^a Cite des 300 Lots. Yahiaoui. 51, rue Harrag Senoussi. 19000 S´etif, Algeria.

*Corresponding author.

Abstract :

The purpose of this work is to prove results concerning the duality theory and to give detailed study on the augmented Lagrangian algorithms and $% \varepsilon $-proximal penalty method which are considered, today, as the most strong algorithms to solve nonlinear differentiable and nondifferentiable problems of optimization. We give an algorithm of primal-dual type, where we show that sequences $\left\{ \lambda ^{k}\right\} _{k}$ and $\left\{ x^{k}\right\} _{k}$ \ generated by this algorithm converge globally, with at least the Slater condition, to $\overline{\lambda }$ and $\overline{x}$. Numerical simulations are given.

Keywords :

Convex programming, augmented Lagrangian, $\varepsilon $% -proximal penalty method, duality, Perturbation, Convergence of algorithms.

DOI :

Article Info :

Received : March 02, 2016; Accepted : September 14, 2016.