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### Quadratic Program (QP)

#### Formulation
- **Objective**: Minimize \((1/2)x^TPx + q^Tx + r\)
- **Subject to**:
  - \(Gx \preceq h\)
  - \(Ax = b\)

#### Properties
- \(P \in S_n^+\), indicating the objective is convex quadratic.
- The goal is to minimize a convex quadratic function over a polyhedron.

#### Diagram
- A shaded polygon labeled \(P\) represents the feasible region.
- The optimal point \(x^*\) is marked within the region.
- Contour lines represent level curves of the objective function.
- A vector \(-\nabla f_0(x^*)\) indicates the direction of the gradient at \(x^*\).

#### Reference
- A. d’Aspremont, Convex Optimization M2, Slide 53/67.
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