SIAM Journal on Optimization
Gauss---Newton method for convex composite optimizations on Riemannian manifolds
Journal of Global Optimization
Convergence analysis of a proximal Gauss-Newton method
Computational Optimization and Applications
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We introduce a notion of quasi regularity for points with respect to the inclusion $F(x)\in C$, where $F$ is a nonlinear Fréchet differentiable function from ${\mathbb{R}}^v$ to ${\mathbb{R}}^m$. When $C$ is the set of minimum points of a convex real-valued function $h$ on ${\mathbb{R}}^m$ and $F'$ satisfies the $L$-average Lipschitz condition of Wang, we use the majorizing function technique to establish the semilocal linear/quadratic convergence of sequences generated by the Gauss-Newton method (with quasi-regular initial points) for the convex composite function $h\circ F$. Results are new even when the initial point is regular and $F'$ is Lipschitz.