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Unformatted text preview: expected value. (For γ > 0, we are willing to
tradeoﬀ an increase in expected cost for a decrease in cost variance). How would you minimize
the risk-sensitive cost? Is this problem a convex optimization problem? Be as speciﬁc as you
(c) We can also minimize the risk-sensitive cost, but with γ < 0. This is called ‘risk-seeking’. Is
this problem a convex optimization problem?
(d) Another way to deal with the randomness in the cost cT x is to formulate the problem as
subject to prob(cT x ≥ β ) ≤ α
Here, α is a ﬁxed parameter, which corresponds roughly to the reliability we require, and
might typically have a value of 0.01. Is this problem a convex optimization problem? Be as
speciﬁc as you can. Can you obtain risk-seeking by choice of α? Explain.
3.11 Formulate the following optimization problems as semideﬁnite programs. The variable is x ∈ Rn ;
F (x) is deﬁned as
F (x) = F0 + x1 F1 + x2 F2 + · · · + xn Fn
with Fi ∈ Sm . The domain of f in each subproblem is dom...
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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