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6.253: Convex Analysis and Optimization
Homework 4
Prof. Dimitri P. Bertsekas
Spring 2010, M.I.T.
Problem 1
Let f : Rn 7! R be the function
n
f (x) =
1X
|xi |p
p
i=1
where 1 < p. Show that the conjugate is
n
f ? (y) =
1X
|yi |q ,
q
i=1
where q is dened by
18.781 Problem Set 5
Thursday, April 5.
Collaboration is allowed and encouraged. However, your writeups should be your own, and you
must note on the front the names of the students you worked with.
Extensions will only be given for extenuating circumstanc
6 856 Randomized Algorithms
David Karger
Handout #22, November 20, 2000 Homework 11, Due 11/27
12
M. R. refers to this text:
Motwani, Rajeez, and Prabhakar Raghavan. Randomized Algorithms. Cambridge: Cambridge University Press, 1995.
1. For basic Markov c
6.253: Convex Analysis and Optimization
Homework 3
Prof. Dimitri P. Bertsekas
Spring 2010, M.I.T.
Problem 1
(a) Show that a nonpolyhedral closed convex cone need not be retractive, by using as an example
the cone C = cfw_(u, v, w) | k(u, v)k w, the recess
2.094
FINITE ELEMENT ANALYSIS OF SOLIDS AND FLUIDS
SPRING 2008
Homework 2
Instructor:
Assigned:
Due:
Prof. K. J. Bathe
02/14/2008
02/21/2008
Problem 1 (20 points):
Consider the disk with a centerline hole of radius 20 shown spinning at a rotational veloci