  The randomized subspace Newton convex methods for the sensor selection
problem are proposed. The randomized subspace Newton algorithm is
straightforwardly applied to the convex formulation, and the customized method
in which the part of the update variables are selected to be the present best
sensor candidates is also considered. In the converged solution, almost the
same results are obtained by original and randomized-subspace-Newton convex
methods. As expected, the randomized-subspace-Newton methods require more
computational steps while they reduce the total amount of the computational
time because the computational time for one step is significantly reduced by
the cubic of the ratio of numbers of randomly updating variables to all the
variables. The customized method shows superior performance to the
straightforward implementation in terms of the quality of sensors and the
computational time.
