Residual subspace evolution strategies for nonlinear inverse problems

Nonlinear inverse problems often feature noisy, non-differentiable, or expensive residual evaluations that make Jacobian-based solvers unreliable. Popular derivative-free optimizers such as natural evolution strategies (NES) or Powell's NEWUOA still assume smoothness or expend many evaluations to maintain stability. Ensemble Kalman inversion (EKI) relies on empirical covariances that require preconditioning and scale poorly with residual dimension.