传统的多核学习方法通常将原问题转换为其对偶问题再进行求解，但直接求解原问题比求解对偶问题有更好的收敛属性． 为此，文中提出了一种在原问题上求解、L P 范数约束的非稀疏多核学习算法，首先采用次梯度和改进的拟牛顿法求解支持向量机(SVM)，然后通过简单计算求解基本核的权系数． 由于拟牛顿法具有二次收敛性，并且不需要计算二阶导数来得到 Hessian 矩阵的逆，因此文中算法具有更快的收敛速度． 仿真结果表明，文中算法不仅具有较好的分类精度和泛化性能，还具有较快的收敛速度及很好的可扩展性．

Traditional multi-kernel learning (MKL) methods mainly solve primal problems in the dual． However，the solving in the primal may result in better convergence property． In this paper，a novel L p -norm-constraint non-sparse MKL method，which optimizes the modal in the primal，is proposed． In this method，firstly，support vector machine (SVM) is solved by means of subgradient and improved quasi-Newton method． Then，basic kernel weights are obtained via simple calculations． As quasi-Newton method is of second-order convergence property and acquires inverse Hessian matrix without computing the second-order derivative，the proposed method is of higher convergence speed than that of conventional ones． Simulated results show that the proposed method is of comparable classifica-tion accuracy，strong generalization capability，high convergence speed and good scalability．