We apply the optimization algorithm developed by Konnov and Krotov Automation and Remote
Control 60, 1427 (1999) to quantum control problems. Using a second order construction, 
we derive a class of monotonically convergent optimization algorithms. We show that for 
most quantum control problems, the second order contribution can be straightforwardly 
estimated since optimization is performed over compact sets of candidate states. 
Generally, quantum control problems can be classified according to the optimization 
functionals, equations of motion and dependency of the Hamiltonian on the control. For 
each problem class, we outline the resulting monotonically convergent algorithm. While a
second order construction is necessary to ensure monotonic convergence in general, for the ’standard’ quantum control problem of a convex final-time functional, linear 
equations of motion and linear dependency of the Hamiltonian on the field, both first 
and second order algorithms converge monotonically. We compare convergence behavior and 
performance of first and second order algorithms for two generic optimization examples.