Many questions of optimization, and optimal control, arise in management,
economics and engineering. An optimum(maximum or minimum) issought for
some function describing the system, subject to constraints on the values ofthe
variables. Often the functions are nonlinear, so more specialized methodsthan
linear programming are required. Inoptimal control, the variablesin the problem
become functions oftime - state and control functions. A state function
could be a path to be followed, or describe sales rate or earnings in a business
model or water level in a water storage system, and the control function
describes what can be controlled, within limits, in order to manage the system.
This subject, as wellas contributing to a large diversity ofapplications, has generated
a great deal ofmathematics and a variety of computational methods.