Abstract: 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．

Key words: multi-kernel learning, quasi-Newton method, alternating optimization, support vector machines