bv_cvxbook_extra_exercises

Bv_cvxbook_extra_exercises

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Unformatted text preview: provided the problem is feasible. It is often useful to explore the set of nearly optimal points. When a problem has a ‘strong minimum’, the set of nearly optimal points is small; all such points are close to the original optimal point found. At the other extreme, a problem can have a ‘soft minimum’, which means that there are many points, some quite far from the original optimal point found, that are feasible and have nearly optimal objective value. In this problem you will use a typical method to explore the set of nearly optimal points. We start by ﬁnding the optimal value p⋆ of the given problem minimize f0 (x) subject to fi (x) ≤ 0, hi (x) = 0, i = 1, . . . , m i = 1, . . . , p, as well as an optimal point x⋆ ∈ Rn . We then pick a small positive number ǫ, and a vector c ∈ Rn , and solve the problem minimize cT x subject to fi (x) ≤ 0, i = 1, . . . , m hi (x) = 0, i = 1, . . . , p f0 (x) ≤ p⋆ + ǫ. Note that any feasible point for this problem is ǫ-suboptimal f...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.

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