bv_cvxbook_extra_exercises

16 312 a matrix fractional function1 show that x b

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 can. (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 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...
View Full Document

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.

Ask a homework question - tutors are online