How often is optimization used vs statistical modeling?

I was wondering if optimization is ever used to solve problems in data science vs using statistical models. I’m sure it depends on the problem entirely, but I’m wondering how often any of you have relied on creating an objective function, creating some constraints and used some sort of linear programming or optimization algorithm to understand parameters vs using statistical modeling methods like regression or any other techniques. Asking because for a math minor course i am wondering if I …

datascience modeling optimization statistical statistical modeling