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.

提出了一种顶点交换方法，用于解决满足广义单纯形约束的强凸二次规划问题。通过对该算法进行严格收敛性分析，证明了它在解决某些重要类别的约束凸优化中的关键作用。为了获得算法执行的可行初始点，还提出并分析了一种高效的半光滑牛顿法，用于计算广义单纯形上的投影。通过一系列广泛的数值实验，展示了所提算法的出色实际性能。我们的理论和数值结果进一步激发了所考虑模型和所提算法的潜在应用。

一类二次规划问题的顶点交换方法