bv_cvxbook_extra_exercises

# 16 312 a matrix fractional function1 show that x b

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Unformatted text preview: expected value. (For γ &gt; 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 can. (c) We can also minimize the risk-sensitive cost, but with γ &lt; 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 minimize β subject to prob(cT x ≥ β ) ≤ α Ax b. 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.

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