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Many problems in computer graphics and vision can be formulated as a nonlinear least squares optimization problem, for which numerous off‐the‐shelf solvers are readily available. Depending on the structure of the problem, however, existing solvers may be more or less suitable, and in some cases the solution comes at the cost of lengthy convergence times. One such case is semi‐sparse optimization problems, emerging for example in localized facial performance reconstruction, where the nonlinear least squares problem can be composed of hundreds of thousands of cost functions, each one involving many of the optimization parameters. While such problems can be solved with existing solvers, the computation time can severely hinder the applicability of these methods. We introduce a novel iterative solver for nonlinear least squares optimization of large‐scale semi‐sparse problems. We use the nonlinear …