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In this paper, we investigate the optimal control problem for the k-FORQ/MCHequation with strong viscosity.We prove the existence and uniqueness of thisequation under the initial and boundary conditions by Galerkin method. Fromthese results and the Lion's theory we deduce the existence of an optimalsolution to the control problem governed by the viscous k-FORQ/MCH equation.Using augmented Lagrangian method, we deduce the first-order necessaryoptimality condition and two second-order sufficient optimality conditions.

On the optimal control problem for the k-FORQ/MCH equation with viscosity