A nonlinear programming problem minimizes an objective over finitely many real variables subject to constraints, with at least one objective or constraint nonlinear. Parametrizing the pulse amplitudes in quantum optimal control produces such a problem. Gradient descent and related local methods exploit differentiability, but a local stationary point need not be a global optimum without additional convexity or other structure.
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Nonlinear programming (NLP) is a branch of mathematical optimization that deals with the optimization of a nonlinear objective function, subject to constraints that may also be nonlinear. In contrast to linear programming, where both the objective function and the constraints are linear (i.e., they can be expressed as a linear combination of variables), nonlinear programming allows for more complex relationships between the variables.