  This paper focuses on the quadratic optimization over two classes of
nonnegative zero-norm constraints: nonnegative zero-norm sphere constraint and
zero-norm simplex constraint, which have important applications in nonnegative
sparse eigenvalue problems and sparse portfolio problems, respectively. We
establish the KL property of exponent 1/2 for the extended-valued objective
function of these nonconvex and nonsmooth optimization problems, and use this
crucial property to develop a globally and linearly convergent projection
gradient descent (PGD) method. Numerical results are included for nonegative
sparse principal component analysis and sparse portfolio problems with
synthetic and real data to confirm the theoretical results.
