Example: pipeline for constant flow rate.
Capital cost pipe diameter, D - maybe should be D0.6 or D0.9.
D-4.75 - assumes friction factor
Typically, capital cost versus operating cost.
|f(x)||- the objective function|
|x||- the decision variable|
Constraints define feasible region.
Minimise f(x) with respect to (w.r.t.) x, subject to (s.t.) ,
Example: (use D instead of x) minimise f(D) = 2.0 D + 0.4 + 0.5 D-4.75 (s.t.) , .
If expression available for derivative..
Nature of each SP at xsp is given by sign of second derivative f''(x):
|+||implies local minimum|
|-||implies local maximum|
Hence local minimum.
Beware of discontinuities
Simple theory assumes that both f(x) and f'(x) are continuous. If not, global minimum may exist at or near a discontinuity in f or f'.
Profit, throughput, reactor conversion,...
`Maximise f(x)' is equivalent to `Minimise -f(x)'.
Without loss of generality, a computer code can treat all problems as minimisations.
Next - Section 5.3.2: Non-gradient Methods
Return to Section 5.3 Index
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Course Organiser Last modified: Tue Aug 25 10:29:53 BST