$$\mathbf{x}=\min_{\mathbf{x}}\Vert{\mathbf{x-m}}\Vert_{2}\\ \text{subject to} \ \Vert\mathbf{x}-\mathbf{c}\Vert_{2}=d, \ \mathbf{Ax}\le \mathbf{b} $$
can this problem be solved analytically or numerically?
$$\mathbf{x}\in\mathbb{R}^{3}$$ $$\mathbf{c}\in\mathbb{R}^{3}$$ $$\mathbf{m}\in\mathbb{R}^{3}$$ $$\mathbf{c}\ \text{is the center of circle in 3D}$$ $$\mathbf{Ax}\le \mathbf{b} \ \text{is the planes which cut the circle}$$
$$\text{this means that i am looking for the circle surface $\mathbf{x}$ which minimize the norm of}\ \mathbf{x}=\min_{\mathbf{x}}\Vert{\mathbf{x-m}}\Vert_{2}$$
$$\text{in or out side of the circle, there is a point}\ \mathbf{m}\ \text{and i want to find}\ \mathbf{x} \ \text{on the surface of the cut circle}$$
Picking a solution to this problem seems like a very easy task and intuitive if i draw this problem in 3-D. But this problem is a non convex problem and seems to be a very difficult problem
thank you