Quadratic program (${\min }_x\{\frac{1}{2}{x}^{T}Qx+c^{T}x:Ax\le b,Ex=f\}$)

A quadratic program is an optimization problem with a quadratic objective and linear equality or inequality constraints. A positive-definite objective Hessian makes it strictly convex and coercive; on a nonempty closed feasible set its minimizer exists and is unique. Such a program resolves tied Lasso knots by constraining tangent signs of currently zero regression coefficients while allowing unrestricted tangents for nonzero ones.