What characterizes a nonlinear optimization problem?

A nonlinear optimization problem is characterized by the presence of at least one nonlinear term in its formulation. This means that the relationships between variables can be represented by nonlinear equations or inequalities, which may involve terms raised to powers, products of variables, or other nonlinear functions.

Linear optimization problems, in contrast, are characterized exclusively by linear relationships, where all equations and inequalities involve only linear terms. The inclusion of nonlinear terms adds complexity to the problem, making it necessary to use different methods or algorithms for solving it compared to linear optimization.

The other choices do not accurately define a nonlinear optimization problem: the presence of only linear terms refers to a linear optimization problem; the assertion that nonlinear problems only solve for minimum values is misleading, as nonlinear problems can seek either maxima or minima; and the statement about involving only binary variables pertains specifically to integer programming problems, which can be either linear or nonlinear depending on the nature of the constraints and objective function.