|Help needed for simple problem
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|Author:||CevicanAnders [ Thu Mar 18, 2021 1:36 pm ]|
|Post subject:||Help needed for simple problem|
I am not a mathematician but I would appeciate some assistance in how to model the following geometrical problem.
We have a rectangle with rounded corners that must fit within a circle (Not necessarily tangent edges of circle).
W Width of rectangle
H Height of rectangle
R Radius of rectangles corner
D Diameter of circle
W [10..100] Continuous or discrete range
H [10..100] Continuous or discrete range
R [1..100] Continuous or discrete range (Deliberately too large)
D [10,12,14,16,20,30] Discrete set
C1 R < 0.5 W
C2 R < 0.5 H
(C3 (W-2R)^2 + (H-2R)^2 <= (D-2R)^2)
Replacing C3 by substitution with the following Constraints
C7 A^2 + B^2 <= C^2
We want to maximize/minimize each variable (typically W, H, R) for each diameter D
If we have understood it correctly, this is a QCLP - a linear objective function (single variable) with a mix of linear/quadratic equality/inequality constraints.
Note: This is just an example and we do know how to solve it manually of course - however we are trying to understand how such a model can be setup and solved in Alglib.
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