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Exercises Consider a feasible region S defined by a set of linear constraints: S = {x...

Exercises

  1. Consider a feasible region S defined by a set of linear constraints:

S = {x : Ax ≤ b}

Prove that S is convex.

  1. Express (2, 2)T as a convex combination of (0, 0)T , (1, 4)T , and (3, 1)T
  1. Determine if f (x1 , x2 ) = 2x12 – 3x1x2 + 5x22 - 2x1 + 6x2

is convex, concave, both, or neither for x Є R2

Math   Advanced-Math   
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