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Smooth and Non-Smooth Problems
Optimization
Smooth and Non-Smooth Problems
When the functions corresponding to the design objectives do not have continuous derivatives
or are not continuous at all, methods for smooth problems (such as the Eldo optimizer SQP
algorithm) will encounter difficulties.
Figure 13-7. Examples of Non-Smooth Problems
It is assumed that the functions are continuous, with continuous derivatives on some domain (or
sufficiently smooth). Figure 13-7 illustrates some of these difficulties:
• Noisy function
The overall trend is plotted with dashed lines. It is related to the effect of features such
as adaptive algorithms and stopping tests in iterative methods inside the simulation. The
noise is not stochastic in such situations.
The Eldo optimizer SQP method will fail to make any progress because local descent
directions may point uphill.
• Non-smooth minimum (not differentiable)
Functions such as ABS(.), MIN(.) or MAX(.) that are not differentiable in the common
sense can represent minor difficulties when you only want to improve the current
solution rather than optimization at full-blown optimality.
• Discontinuous
This leads to serious difficulties. It usually involves functions that are not numerical in
nature, or the discontinuities may be the result of features such as table look-ups and
switches.
• Undefined
Eldo® User's Manual, 15.3 631