中文摘要：

在这篇论文，分离吝啬变化的模型在凹面办理费用下面为公事包选择被考虑。由使用 Cholesky 分解技术，获得一个可分离的混合整数的反对变化矩阵非线性的优化问题被分解。基于 Lagrangian，松驰当时是的一个 brand-and-bound 算法求婚了。计算结果从 US 证券市场与随机产生的数据和那些为测试问题被报导。

英文摘要：

In this paper, the discrete mean-variance model is considered for portfolio selection under concave transaction costs. By using the Cholesky decomposition technique, the convariance matrix to obtain a separable mixed integer nonlinear optimization problem is decomposed. A brand-and-bound algorithm based on Lagrangian relaxation is then proposed. Computational results are reported for test problems with the data randomly generated and those from the US stock market.