what would be good methods (and/or software packages) to try for solving a problem minimizing a quadratic function $f(x) = \sum_{i=1}^N{(x_i - y_i)^2}$, s.t. $0 \leq x_i \leq 1$, and there are more constraints some of which are non-linear (and non-differentiable), e.g. $\sum_i x_i \mathbf{1}_{x_i>a} < b$ ? I am thinking about $N \approx 100$. FWIW, Matlab is apparently using an active set method, similar to that of Gill et al., which has somewhat uneven performance.
Minimizing a quadratic function with nonlinear constraints
optimization;nonlinear programming
If you have nonsmooth constraints, it is no help that you have a convex quadratic objective. You need a constrained nonsmooth solver. See my web pagehttp://www.mat.univie.ac.at/~neum/glopt/software_l.html#nonsm for suitable software.