What algorithms are applicable to solve a inequality constraint Quadratic Optimization?

179 Views Asked by At

Suppose that we have a quadratic optimization problem $$(QP) \qquad \min \lbrace\frac{1}{2}x^TQX+ q^TX\rbrace $$ s.t. $$AX=a;$$ $$BX\le b;$$ $$X \ge 0;$$ where $Q \in \mathbb{R}^{n \times n}$ symmetric and semi-positive definite, $A \in \mathbb{R}^{m_1 \times n}$, $B\in \mathbb{R}^{m_2 \times n}$ and $m_1 \le n$ and $m_2 \le n$.

What type of algorithm is appropriate to solve a medium-size instance of this problem? I know for this type of QP, inequality constraint QP, two classes of solution algorithms exist; the active-set method and the interior point method. I am wondering if you can offer a source that introduces an appropriate and easy-to-understand algorithm for solving this QP with real application.