The standard form of a nonlinear constrained optimization problem consists of one objective function:

(36–1)

which is subject to the following constraints:

In the previous equations, represents a set of design variables, and and are the number of inequality and equality constraints, respectively. is a component of one of a number () of design variables, with lower and upper bounds and .

The objective and constraint functions may be linear or nonlinear. It is possible that there are no inequality or equality constraints defined for a problem (that is, it may be unconstrained). On the other hand, all problems need to have defined side constraints.

If the optimization problem is a maximization of , Ansys Polyflow will automatically change it to minimize . Similarly, Ansys Polyflow will automatically change inequality constraints of the form to be .

It is assumed that the set of design variables is continuous between the lower and the upper bounds. The number of design variables must be reasonably small (that is, less than 20).

The optimizer has only one objective function (). If you want to address multiple objective functions, you must either combine them into a single objective function, or optimize them individually (see Objective Functions for further details). It is assumed that is normalized, which means the initial value of is 1.