Optimization theory is a useful tool for engineers who must address goal-directed problems. Engineering optimization problems can roughly be classified into two types: optimal control problems and optimal design problems. In the former, the aim is to determine the optimal controls that will maximize system performance, often subject to penalty on control effort. This strategy may involve feedforward and/or feedback mechanisms. In optimal design the problem is to determine a set of design parameters to that best meet a extremize a criterion that is typically a function of weighted sum of subcriteria and constraints. For all but the simplest problems, the problem must be solved numerically.

There are four classic components to the numerical optimization problem:

• System to be controlled (e.g., the health status and functional impairments of the person)

• Performance criteria to be maximized/minimized (e.g., maximizing benefits while minimizing costs)

• Controls to adjust (e.g., an intervention strategy)

• Algorithm that searches for the set of controls that, when applied to the system, cause the performance criteria to be extremized

As seen in the figure and expressed by the definition of "algorithm," there are clear, structured relations between these components.

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