Trust-region methods for nonconvex sparse recovery optimization

We solve the ℓ
₂
-ℓ
_p
sparse recovery problem by transforming the objective function into an unconstrained differentiable function and apply a limited-memory trust-region method. Unlike gradient projection-type methods, which uses only the current gradient, our approach uses gradients from previous iterations to obtain a more accurate Hessian approximation. Preliminary numerical experiments with simulated compressive sensing 1D data are provided to illustrate that our proposed approach eliminates spurious solutions more effectively while improving the computational time to converge in comparison to standard approaches.