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February 27th, 2014, 04:56 AM   #1
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replace indicator functions with convex conjugates?

I'm trying to get rid of the indicator functions in the following
convex optimization problem.

Let be a countable set of convex subsets of ,
and assume that the vectors are given for some
.



where and if and if

So here's my approach so far:

1. Getting rid of :

subject to:



2. Dual:

subject to


3. At this point I'd like to get rid of the indicator functions, perhaps using their convex conjugates.
But I'm a bit stuck.
Any ideas?

Thanks!
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