I am looking for an algorithm to solve an equality constrained elastic net.
There are two adaptations I need to make to the standard elastic net. First the objective function includes a quadratic term, and second the sum of my coefficients is constrained to be equal to one.
My objective function would be:
minimize $\quad x^TAx + \lambda \; (\alpha ||x||_1 + (1- \alpha ) ||x||_2^2) $
subject to $ \ \ \sum_{i=1}^N x_i = 1 $
