forum.alglib.nethttp://forum.alglib.net/ Help needed for simple problemhttp://forum.alglib.net/viewtopic.php?f=2&t=4378 Page 1 of 1

 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 rectangleH Height of rectangleR Radius of rectangles cornerD Diameter of circleApproximate domains:W [10..100] Continuous or discrete rangeH [10..100] Continuous or discrete range R [1..100] Continuous or discrete range (Deliberately too large)D [10,12,14,16,20,30] Discrete setConstraintsC1 R < 0.5 WC2 R < 0.5 H(C3 (W-2R)^2 + (H-2R)^2 <= (D-2R)^2)Replacing C3 by substitution with the following ConstraintsC4 A=W-2RC5 B=H-2RC6 C=D-2RC7 A^2 + B^2 <= C^2We want to maximize/minimize each variable (typically W, H, R) for each diameter DIf 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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