中文摘要：

在投资过程中，交易成本是不能忽视的。一般情况下，交易量较小时，单位交易成本较大；随着交易量的增加，单位交易成本不断减少；当交易量大于某值时，单位交易成本不变。提出了交易成本函数为二次分段凹函数的均值-方差投资组合模型，并结合不等式组的旋转算法和分枝定界法求解。最后，采用中国证券市场的实际数据，运用自编程序计算出不同期望收益率所对应的最优投资比例，从而为投资者提供决策支持。

英文摘要：

The transaction costs can＇t be ignored in investment. When the transaction volumes are small, the unit cost is big. When the transaction volumes are increasing, the unit cost is decreasing. When the transaction volumes are bigger than some value, the unit cost doesn＇t change. A mean-variance portfolio selection model with qadratic subsection concave transaction costs is proposed and the pivoting algorithm and branch bound algorithm are used to solve it. At last, the optimal investment strategies of different expected rates through Chinese security market data is calculated.