I'm a computer science student. Please I need a help in solving a constrained normalized quadratic function. I'm familiar with solving quadratic constrained optimization function with matlab by providing a symmetric matrix and a vector as inputs for quadprog matlab function. Now, I encountered an other form of quadratic function described as follows:
$$ \min_{0 \leq \alpha \leq C} \left( \frac{1}{2} \frac{\alpha^tB\alpha}{\alpha1_N}+ b^t\alpha \right)$$
where $ b^t=\left[b_1,...,b_N\right] $ is a parameter vector. $B=\left[b_ij\right] $ is a symmetric positive matrix of parameters. $ \alpha 1_N = \sum_{i=1}^{N} \alpha_i $. $0 \leq \alpha \leq C $ mean that $ \forall i \in {1,...,n}, 0 \leq \alpha_i \leq C $. I don't know how I can deal with such function. Can I rewrite the normalized quadratic function as a quadratic function? Is there any tutorial, any link describing the different mathematical steps for solving such problem in order to make the necessary implementation?
thanks.