  A vertex exchange method is proposed for solving the strongly convex
quadratic program subject to the generalized simplex constraint. We conduct
rigorous convergence analysis for the proposed algorithm and demonstrate its
essential roles in solving some important classes of constrained convex
optimization. To get a feasible initial point to execute the algorithm, we also
present and analyze a highly efficient semismooth Newton method for computing
the projection onto the generalized simplex. The excellent practical
performance of the proposed algorithms is demonstrated by a set of extensive
numerical experiments. Our theoretical and numerical results further motivate
the potential applications of the considered model and the proposed algorithms.
