Quadratic Program Direct Substitution

Speedup quadratic program (quadprog) calls, by first performing direct substitution of any equality constraints.

Solves a quadratic program using direct substitution of the equality constraints as opposed to passing the equality constraints to the QP-solver (which uses the Lagrange multiplier method to satisfy quality constraints). This method works by finding the null space of the equality constraints and solving a smaller QP for a solution within that null space.

This method is faster for some problems. For example, running quadprogds_test.m on Macbook A1, with 2000 variables in the QP and 400 equality constraints, this method took 0.9s versus 2.2s, a speedup 2.4x.