Let $a,b,c,d$ be constants in the interval $[-1,1]$. Let $A$ be the minimum of the following three numbers: $$\max\{2-a-c, |b-d|\},$$ $$\max\{2-b-c, 2-a-d, 2-b-d\},$$ $$\max\{2+b-c, 2-a+d, 2+b+d\}.$$ Is there a neater way to express $A$?
A minimum of three maximums
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analysis
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0Related: http://math.stackexchange.com/questions/110808/a-minimization-problem-for-a-function-involving-maximum – 2012-02-21