Suppose that is such that , we have . Prove that S is convex. Here X is a Hilbert space and means the proximal normal cone.

It is urgent for me to get the answer. Thank you very much!

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- Jun 24th 2013, 06:12 AMwatashi618Nonsmooth analysis Prove a set to be convex
Suppose that is such that , we have . Prove that S is convex. Here X is a Hilbert space and means the proximal normal cone.

It is urgent for me to get the answer. Thank you very much! - Jun 25th 2013, 01:25 AMchiroRe: Nonsmooth analysis Prove a set to be convex
Hey watashi618.

Are there results that show if an inner product space is convex, then any subspace is also convex as well? - Jun 25th 2013, 09:01 PMwatashi618Re: Nonsmooth analysis Prove a set to be convex
Any subspace is convex, but here S is just a subset of X, not a subspace of X.

- Jun 25th 2013, 11:20 PMchiroRe: Nonsmooth analysis Prove a set to be convex
Can you make it into the appropriate inner product space and prove the corresponding set with its inner product is a sub-inner product space?

- Jun 26th 2013, 12:01 AMwatashi618Re: Nonsmooth analysis Prove a set to be convex
I think it is very difficult to do this.