TEST BANK FOR Convex Optimization 1st Edition By Stephen Boyd
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Exam (elaborations) TEST BANK FOR Convex Optimization 1st Edition By Stephen Boyd (Solution Manual)
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Let C Rn be a convex set, with x1; : : : ; xk 2 C, and let 1; : : : ; k 2 R satisfy i 0,
1 + + k = 1. Show that 1x1 + + kxk 2 C. (The de nition of convexity is that
this holds for k = 2; you must show it for arbitrary k.) Hint. Use induction on k.
Solution. This is readily shown by induction from the de nition of convex set. We illustrate
the idea for k = 3, leaving the general case to the reader. Suppose that x1; x2; x3 2 C,
and 1 + 2 + 3 = 1 with 1; 2; 3 0. ...
Exam (elaborations)
Exam (elaborations) TEST BANK FOR Convex Optimization 1st Edition By Stephen Boyd (Solution Manual)
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Let C Rn be a convex set, with x1; : : : ; xk 2 C, and let 1; : : : ; k 2 R satisfy i 0, 1 + + k = 1. Show that 1x1 + + kxk 2 C. (The de nition of convexity is that this holds for k = 2; you must show it for arbitrary k.) Hint. Use induction on k. Solution. This is readily shown by induction from the de nition of convex set. We illustrate the idea for k = 3, leaving the general case to the reader. Suppose that x1; x2; x3 2 C, and 1 + 2 + 3 = 1 with 1; 2; 3 0. ...
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