Hybrid Algorithm for System of Nonlinear Monotone Equations Based on the Convex Combination of Fletcher-Reeves and a New Conjugate Residual Parameters: Kamaluddeen Umar Danmalam, Hassan Mohammad, Auwal Bala Abubakar, Aliyu Muhammed Auwal - Team, Support (Thai Journal of Mathematics, 2020)
In this paper, based on the projection strategy of Solodov and Svaiter (1998,Reformulation: Nonsmooth, Piecewise Smooth, Semismooth, and Smoothing Methods (M. Fukushima & L. Qi eds) Dordrecht: Kluwer, pp. 355-369), we present a hybrid conjugate residual algorithm for nonlinear monotone equations with convex constraints. The parameter is computed as a convex combination of the Fletcher-Reeves (FR) and a new conjugate residual parameters. Furthermore, the convex combination parameter is chosen in such a way that the search direction satisfied the descent property, independent of any line search. The global convergence of the proposed hybrid algorithm was given under some suitable conditions. The proposed approach is shown to be efficient and promising based on the preliminary computational experiments performed on some standard problems.