Question

A nonlinear optimization problem is any optimization problem in which at least one term in the objective function or a constraint is nonlinear. True or false?

Answer 1

Answer:

Yes

Explanation:

A nonlinear optimization problem is indeed a optimization problem in which there are nonlinear elements involved either as the objective function or one or more constraints may be nonlinear also. Let me show you an example. Let optimize de following function:

$f(x) = x_{1} +x_{2}$

These are the constraints:

$x_{1} \geq 0\\x_{2} \geq 0\\\\x_{1} ^{2} + x^{2}_{2} \geq 1$

The last constraint consists on nonlinear elements, so this problem in fact a nonlinear optimization problem.