Correct terminology for optimization problem

Question

An optimization problem aims to minimize the sum of a variable u over a time-series. It is made of three variables that are in a linear relationship. Two binary variables

$$x_1, x_2, \dots x_n$$

and

$$u_1, u_2, \dots u_n$$

and a continuous variable

$$y_1, y_2, \dots y_n$$

The objective function is $$minimize \sum u$$

s.t. $$y_{n}=y_{n-1}+ u_{n}\cdot C$$ $$y_{n}\geq x_{n} \cdot M$$ $$0<y_{n}<2\cdot M$$ $$x_{n}\wedge u_{n} \in \{0,1\}$$

Would "Binary linear programming problem" be the correct terminology to describe this?

Answer 1

The correct contemporary term is mixed integer linear optimization.