How to maximize $\sum_{i=1}^N \log(1+a_i x_i^2) \text{ s.t.} \sum_{i=1}^N x_i= 1,x_i \geq 0$

Question

How to maximize $\sum_{i=1}^N \log(1+a_i x_i^2) s.t. \sum_{i=1}^N x_i= 1,x_i \geq 0$? The objective function is non-convex. Is there any tutorial or solution about how to deal with such problem ? Thank you!