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.

翻译：本文针对广义单纯形约束下的强凸二次规划问题，提出了一种顶点交换求解方法。我们对所提算法进行了严格的收敛性分析，并论证了其在求解若干重要类别约束凸优化问题中的核心作用。为获得执行算法的可行初始点，我们还提出并分析了一种用于计算广义单纯形投影的高效半光滑牛顿法。通过一系列广泛的数值实验，验证了所提算法优异的实际性能。我们的理论与数值结果进一步激发了所研究模型及所提算法的潜在应用前景。