# Least Square with quadratic constraint [closed]

I have the following problem:For $$\theta \in \mathbb{C}^{n\times1}$$, $$\quad$$ $$Y=X\theta+W$$

where $$W \in \mathbb{C}^{m\times1}$$ is the complex additive white Gaussian noise. $$X \in \mathbb{C}^{m\times n},Y \in \mathbb{C}^{m\times 1}$$ are known. I'd like to solve the following problem:

$$\qquad$$ $$\mathop{\arg\min}_{\theta} \ \ \mathrm{J} (\theta) = \|Y-X\theta\|^2$$

$$\qquad$$ subject to: $$\ \ \theta^TA\theta = 0$$

where $$A \in \mathbb{R}^{n\times n}$$ is known, $$T$$ denote the transpose. Can I solve this problem by Lagrange multipliers and how to do this? And how to get a close-form solution like Least Square with linear equality constraints?

Thanks