2-D Box Volume - Intro

2-D Box Volume - Intro - Maximum Box Volume vol( a , b ) :=...

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Maximum Box Volume vol a b , ()a b 2 := <= Maximize Volume g 1 ab , ()2 a 2b + 11 := <= Constraint 1 g 2 , a b + 8.5 := <= Constraint 2 Optimization problems are written in terms of minimizing the objective function. In order to maximize box volume, minimize the negative the volume: f(a,b) = -vol(a,b) To use the exterior penalty function method, write the objective function and the constraints in the form of a single pseudo-objective function. R5 := pab , ( ) vol a b , () R Φ g 1 , g 1 , 2 + R Φ g 2 , g 2 , 2 + := p a1 := b1 := minimize p a , b , 1.962 3.923 =
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Note that there is no requirement for a and b to be positive. Mathematically, this is no problem, but physically, it doesn't make sense.
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2-D Box Volume - Intro - Maximum Box Volume vol( a , b ) :=...

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