Considering an optimization problem can have a minimization or maximization objective function, which of the following statements is true?

Group of answer choices

The optimal objective value of the LP relaxation model of an integer programming $($IP$)$ model always gives an upper$-$bound to that of the IP$.$

The optimal solution to an integer linear programming problem is always a global optimal solution.

The optimal objective value of the LP relaxation model of an integer programming $($IP$)$ model always gives a lower$-$bound to that of the IP$.$

The optimal solution to a nonlinear programming problem is always a global optimal solution.