Given vectors $\mathbf{q}, \mathbf{n}_1, \mathbf{n}_2,\dots, \mathbf{n}_m \in \mathbb{R}^3$,
$$\begin{array}{ll} \underset{\mathbf{p} \in \mathbb{R}^3}{\text{minimize}} & f(\mathbf{p}) = \left[\mathbf{q}^\mathrm{T}\mathbf{p}\right]^2\\ \text{subject to} & \mathbf{p}^\mathrm{T} \mathbf{p} = 1\\ & \mathbf{n}_i^\mathrm{T} \mathbf{p} \ne 0, \quad \forall 1 \le i \le m\end{array}$$
Do you know any optimization method using which this problem can be solved?