  In this paper, we consider the sparse least squares regression problem with
probabilistic simplex constraint. Due to the probabilistic simplex constraint,
one could not apply the L1 regularization to the considered regression model.
To find a sparse solution, we reformulate the least squares regression problem
as a nonconvex and nonsmooth L1 regularized minimization problem over the unit
sphere. Then we propose a geometric proximal gradient method for solving the
regularized problem, where the explicit expression of the global solution to
every involved subproblem is obtained. The global convergence of the proposed
method is established under some mild assumptions. Some numerical results are
reported to illustrate the effectiveness of the proposed algorithm.
