  The energy needed in controlling a complex network is a problem of practical
importance. Recent works have focused on the reduction of control energy either
via strategic placement of driver nodes, or by decreasing the cardinality of
nodes to be controlled. However, optimizing control energy with respect to
target nodes selection has yet been considered. In this work, we propose an
iterative method based on Stiefel manifold optimization of selectable target
node matrix to reduce control energy. We derive the matrix derivative gradient
needed for the search algorithm in a general way, and search for target nodes
which result in reduced control energy, assuming that driver nodes placement is
fixed. Our findings reveal that the control energy is optimal when the path
distances from driver nodes to target nodes are minimized. We corroborate our
algorithm with extensive simulations on elementary network topologies, random
and scale-free networks, as well as various real networks. The simulation
results show that the control energy found using our algorithm outperforms
heuristic selection strategies for choosing target nodes by a few orders of
magnitude. Our work may be applicable to opinion networks, where one is
interested in identifying the optimal group of individuals that the driver
nodes can influence.
