Quadratic optimizer with linear constraints

Summary:

Create a new function to perform quadratic optimization.

Description:

The goal is to maximize a function subject to a set of equality and inequality constraints. This is a generalization of the Lagrange optimization problem, sometimes termed the Karush–Kuhn–Tucker problem. The proposed feature solves this problem when the function we wish to optimize is quadratic. See http://discourse.mc-stan.org/t/quadratic-optimizier/4405 for more details.

The target function has the form: f(x) = x' H x + v x, where H is a matrix and v a vector. For starters, I want to implement the case where there is a linear constraint on x of the form Ax = b, and x > 0. We can then think of generalizations.

The call to the solver has the form a = quadratic_optimizer(H, v, A, b, theta, delta), where H, v, A, and b are all functions of parameters theta and data delta. Are there features in C++11 to make this easier to implement? Right now, my plan is to mimic what was done for the algebraic and the ODE solver.

Additional Information:

I can think of a few applications for this optimizer; the current motivating problem is in econometrics, brought forth Shosh Vasserman.

Current Version:

v2.17.0