The statements involving \( g(\vx) \) and \( h(\vx) \) require the variable \( \vx \) to satisfy certain conditions.
These statements are known as constraints.
A problem devoid of constraints is unconstrained, otherwise it is a constrained optimization problem.
Specifically, the constraints \( g(\vx) = \va \) are known as the equality constraints.
The constraints \( h(\vx) \ge \vb \) are known as inequality constraints.
The set of all input values \( \vx \) that satisfy the constraints is known as the feasible set.
Note that in unconstrained optimization problems, the feasible set is unbounded.
So, the goal of optimization is to discover the least value of the objective function attainable using the elements of the feasible set as input.