An Improved DFP Method for Solving Convex Constrained Monotone Equations with Application in Image Restoration

In this paper, we embed the memoryless Davidon–Fletcher–Powell (DFP) updating formula with an additional term to propose an improved memoryless DFP formula that guarantees a sufficient descent property irrespective of the line search strategy. We also proposed an improved memoryless DFP algorithm for solving convex-constrained monotone nonlinear equations in connection with the projection technique. The global convergence of this algorithm is analyzed and proved using some mild assumptions. Detailed numerical experiments on solving the monotone nonlinear equations, unconstrained optimization problems, and the image restoration problem showed that the algorithm is robust and efficient compared with the existing ones. This improved version of the DFP formula can also be applied to solve problems that require quasi-Newton updates and their approximations in science and engineering.