Let x i , i = 1, . . . , n, be given real numbers, which
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Let xi, i = 1, . . . , n, be given real numbers, which we assume without loss of generality to be ordered as x1 ≤ x2 ≤ .........≤ xn, and consider the scalar equation in variable n that we encountered in Section 12.3.3.3:
1. Show that f is continuous and strictly decreasing for ν ≤ xn.
2. Show that a solution ν* to this equation exists, it is unique, and it must belong to the interval
3. This scalar equation could be easily solved for n using, e.g., the bisection method. Describe a simpler, “closed-form” method for finding the optimal n.
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Related Book For
Optimization Models
ISBN: 9781107050877
1st Edition
Authors: Giuseppe C. Calafiore, Laurent El Ghaoui
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