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6/3/2017
The inverse problem
A simple optimization problem:
“A manufacturer needs to make a cylindrical can that will hold 1.5
liters of liquid. Determine the dimensions of the can that will
minimize the amount of material used and as such the
COST
of its
construction.”
“The search for the best independent
variable value which results in minimal cost”
Minimise A
3000
r
2
r
2
19
start
r=18
A=2206
⇒ ℎ =
1500
ଶ
The analytic result is
6.20350491
r=16
A=1799
r=13
A=1294
r=10
A=929
r=6
A=727
r=4
A=851
Optimization can involve:
Intensity profiles
Beam weights, segment weights
Beam angles (gantry angle, couch angle)
Number of beams
Energy (especially in charged particle therapy)
Type of radiation (photons, electrons, ...)
20
The inverse problem
Independent variables