Globally and Quadratically Convergent Algorithm for Minimizing the Sum of Euclidean Norms

In this paper, we propose a new QP-free method, which ensures the feasibility of all iterates, for inequality constrained optimization. The method is based on a nonsmooth equation reformulation of the KKT optimality condition, by using the Fischer--...

We consider the problem of minimizing a sum of Euclidean norms. $$F(x) = \sum\nolimits_{i = 1}^m {||r_i } (x)||$$ here the residuals {ri(x)} are affine functions fromRn toR1 (nź1ź2,m>-2). This arises in a number of applications, including single-and ...

We present a primal–dual augmented Lagrangian method to solve an equality constrained minimization problem. This is a Newton-like method applied to a perturbation of the optimality system that follows from a reformulation of the initial problem by ...