Projected gradient iteration for nonlinear operator equation

In this paper, we use a projected gradient algorithm to solve a nonlinear operator equation with ^ℓp-norm (1<p≤2) constraint. Gradient iterations with ^ℓp-norm constraints have been studied recently both in the context of inverse problem and of compressed sensing. In this paper, the constrained gradient iteration is implemented via a projected operator. We establish the ^ℓ2-norm convergence of sequence constructed by the constrained gradient iteration when p∈(1,2]. The performance of the method is testified by a numerical example.