Convert cost function into quadratic constraints

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My objective function and constraints

I've provided the problem and the objective function and constraints I wrote. I'm having problems changing the objective function into quadratic constraints.

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I think you mixed up the conditions for the constraints and the objective function.

For the objective function, you want to minimize the $l_1$ distance, of which it can be converted to a linear form.

For the constraints, we should use $l_2$ distance for the antenna constraint