Variable Projection for NonSmooth Problems

Variable projection solves structured optimization problems by completely minimizing over a subset of the variables while iterating remaining variables. Over past 30 years, technique has been widely used, with empirical and theoretical results demonstrating both greater efficacy stability compared to competing approaches. Classic examples have exploited closed-form projections smoothness objective function. We extend approach that include nonsmooth terms, develop an inexact adaptive algorithm subproblems inexactly iterative methods, analyze its computational complexity. Finally, we illustrate effectiveness numerical examples. Code reproduce is available at https://github.com/TristanvanLeeuwen/VarProNS.