A MODIFIED LIU-STOREY-CONJUGATE DESCENT HYBRID PROJECTION METHOD FOR CONVEX CONSTRAINED NONLINEAR EQUATIONS AND IMAGE RESTORATION

We present an iterative method for solving the convex constraint nonlinear equation problem. The method incorporates the projection strategy by Solodov and Svaiter with the hybrid Liu-Storey and Conjugate descent method by Yang et al. for solving the unconstrained optimization problem. The proposed method does not require the Jacobian information, nor does it require to store any matrix at each iteration. Thus, it has the potential to solve large-scale non-smooth problems. Under some standard assumptions, the convergence analysis of the method is established. Finally, to show the applicability of the proposed method, the proposed method is used to solve the ℓ₁-norm regularized problems to restore blurred and noisy images. The numerical experiment indicates that our result is a significant improvement compared with the related methods for solving the convex constraint nonlinear equation problem.