Accelerated Sparse Recovery via Gradient Descent with Nonlinear Conjugate Gradient Momentum

This paper applies an idea of adaptive momentum for the nonlinear conjugate gradient to accelerate optimization problems in sparse recovery. Specifically, we consider two types minimization problems: a (single) differentiable function and sum non-smooth function. In first case, adopt fixed step size avoid traditional line search establish convergence analysis proposed algorithm quadratic problem. acceleration is further incorporated with operator splitting technique deal second case. We use convex $$\ell _1$$ nonconvex _1-\ell _2$$ functionals as case studies demonstrate efficiency approaches over methods.