A Gauss-Newton method for convex composite optimization

An extension of the Gauss-Newton method for nonlinear equations to convex composite optimization is described and analyzed. Local quadratic convergence is established for the minimization of hℝoslash;F under two conditions, namely h has a set of weak sharp minima, C, and there is a regular point of the inclusion F(x)∈C. This result extends a similar convergence result due to Womersley which employs the assumption of a strongly unique solution of the composite function hℝoslash;F. A backtracking line-search is proposed as a globalization strategy. For this algorithm, a global convergence result is established, with a quadratic rate under the regularity assumption.