In general, there are three fundamental parts of an optimization problem — the control variables, the objective function and, optionally, constraints.

The optimization problem is to find the value of the control variables that minimizes (or maximizes) the objective function, subject to a number of constraints. The constraints collectively define a set, the feasible set, of permissible values for the control variables.

The Optimization Study together with The Optimization Interface provide a framework for specifying and solving general optimization problems. The objective function and constraints can depend indirectly on the control variables via the solution of a multiphysics model. See PDE-Constrained Optimization.