I have a (slightly simplified) model of the following form:
$Y=c_1X_1 + c_2X_2 + \epsilon$ subject to the constraint $0\leq c_1\leq c_2$.
The distribution of $\epsilon$ is actually not important to me - fitting the curve by least squares is all I care about (for a volatility surface parameterization).
What is the best approach to solving this with deterministic results (i.e. not using iterative techniques dependent on starting points etc.).
I am working in C++ and I have Armadillo for my linear algebra library.
I am comfortable with python's libraries as well and R if necessary, but ultimate implementation will be C++.