Trust region algorithm for nonsmooth optimization (Q1366819)

Minimization of a composite function \(h(f(x))\) is considered, where \(f:\mathbb{R}^n\to\mathbb{R}^m\) is a locally Lipschitzian function, and \(h:\mathbb{R}^m\to\mathbb{R}\) is a continuously differentiable convex function. The theory of the trust region algorithm for nonsmooth optimization given by Fletcher, Powell, and Yuan is extended to this case. The trust region algorithm and its global convergence are studied. Finally, some applications on nonlinear and nonsmooth least-squares problems are also given.