Derivative-free RMIL conjugate gradient method for convex constrained equations

Abdulkarim Hassan Ibrahim, Abor Isah Garba, Halima Usman, Jamilu Abubakar, Auwal Bala Abubakar

Abstract

An efficient method for solving large scale unconstrained optimization problems is the conjugate method. Based on the conjugate gradient algorithm proposed by Rivaie, Mohd, et al. ("A new class of nonlinear conjugate gradient coefficients with global convergence properties." Applied Mathematics and Computation 218.22 (2012): 11323-11332.), we propose a spectral conjugate gradient algorithm for solving nonlinear equations with convex constraints which generate sufficient descent direction at each iteration. Under the Lipschitz continuity assumption, the global convergence of the algorithm is established. Furthermore, the propose algorithm is shown to be linearly convergent under some appropriate conditions. Numerical experiments are reported to show the efficiency of the algorithm.