  This paper is intended to solve the nonconvex $\ell_{p}$-ball constrained
nonlinear optimization problems. An iteratively reweighted method is proposed,
which solves a sequence of weighted $\ell_{1}$-ball projection subproblems. At
each iteration, the next iterate is obtained by moving along the negative
gradient with a stepsize and then projecting the resulted point onto the
weighted $\ell_{1}$ ball to approximate the $\ell_{p}$ ball. Specifically, if
the current iterate is in the interior of the feasible set, then the weighted
$\ell_{1}$ ball is formed by linearizing the $\ell_{p}$ norm at the current
iterate. If the current iterate is on the boundary of the feasible set, then
the weighted $\ell_{1}$ ball is formed differently by keeping those zero
components in the current iterate still zero. In our analysis, we prove that
the generated iterates converge to a first-order stationary point. Numerical
experiments demonstrate the effectiveness of the proposed method.
