Hybrid spectral algorithm under a convex constrained to solve nonlinear equations

Abstract

The hybrid spectral technique is the main and important part of optimization and has many numerical applications to solve nonlinear equations with convex constrained. This paper combines a new hybrid spectral method in addition to the projection technique with a new line search under convex constraints. This work proved the global convergence of the new suggested technique under some lemmas and assumptions. Also, this new technique holds many important results such as the sufficient descent property and the new search direction. The numerical experiments show the efficiency and competitiveness of the new technique compared with the other two famous methods.