In the optimization problem with $2$ dependent decision variables, is it possible to reduce the objective function to a problem with one variable and enforce the relation between variables as an equality constraint?
For example, suppose we aim to maximize an objective function $f(q_1,q_2)$ with two correlated variables $q_1$ and $q_2$ (such as weight and size) and their relation is: $q_1=g(q_2)$. Is it correct to keep $q_1$ in the objective function and have "maximize $f(q_1)$" and add "$q_1=g(q_2)$" as a constraint? Is it correct to have such constraint, theoretically?