Projected gradient iteration for nonlinear operator equation

Abstract

In this paper, we use a projected gradient algorithm to solve a nonlinear operator equation with ℓ p -norm (1 < p ≤ 2) constraint. Gradient iterations with ℓ p -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 ℓ 2 -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.