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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.
- Fall '13
- The Aeneid