Exercise 6.3.8

Answers

  • ∥(x1,x2,x3)∥1 = |x1| + |x2| + |x3|≤ 2: if we consider the cases that x1,x2,x3 can separately be positive and negative, we see that there are 23 = 8 combinations for the constraint. That is:

x1 + x2 + x3 ≤ 2 x1 + x2 − x3 ≤ 2 x1 − x2 + x3 ≤ 2 x1 − x2 − x3 ≤ 2 − x1 + x2 + x3 ≤ 2 − x1 + x2 − x3 ≤ 2 − x1 + x2 + x3 ≤ 2 − x1 − x2 − x3 ≤ 2

∥x∥∞≤ 2 is equivalent to |xi|≤ 2 for i = 1,2,3.

x1 ≤ 2,x2 ≤ 2,x3 ≤ 2 x1 ≤ 2,x2 ≤ 2,−x3 ≤ 2 x1 ≤ 2,−x2 ≤ 2,x3 ≤ 2 x1 ≤ 2,−x2 ≤ 2,−x3 ≤ 2 − x1 ≤ 2,x2 ≤ 2,x3 ≤ 2 − x1 ≤ 2,x2 ≤ 2,−x3 ≤ 2 − x1 ≤ 2,−x2 ≤ 2,x3 ≤ 2 − x1 ≤ 2,−x2 ≤ 2,−x3 ≤ 2
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2020-03-20 00:00
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