Hybrid conjugate gradient method for a convex optimization problem over the fixed-point set of a nonexpansive mapping (Q1016416)

The author considers the problem of minimizing a continuously differentiable strongly convex function over the set of fixed points of a non-expansive mapping in a Hilbert space and proposes a two-step iterative procedure to find its solution. On the one hand, this procedure extends the known conjugate gradient and heavy ball type schemes. On the other hand, it extends the so-called hybrid gradient methods. The strong convergence to a solution is established.