Equality-Constrained Quadratic Programs

Resources: page=451, Ch 16.1

---

Given

Quadratic Programming Problem on Standard Form

$$\underset{x\in {\mathbb{R}}^n}{\min }\frac{1}{2}{x}^{T}Gx+c^{T}x,s.t.\{\begin{array}{l}{a}_i^{T}x=b_i,i\in \mathcal{E}\\ a_i^{T}x\ge b_i,i\in \mathcal{I}\end{array}$$

Link to original

But we only have equality constraint, thus getting

$$Ax=b$$

Where $A$ is the $m\times n$ Jacobian of constraints (with $m\le n$).

The KKT system for the equality-constrained QP is

Link to original