KKT conditions for nonsmooth convex problems

Asked Mar 05 '14 at 00:43

Active Oct 05 '19 at 08:49

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What are the KKT conditions for a non-smooth convex function? Is the vanishing gradient of Lagrangian, replaced by $0$ in sub-differential of the Lagrangian, and all other things remain the same?

I suppose that will give necessary and sufficient optimality condition assuming duality gap is zero, right?

edited Oct 05 '19 at 08:49

Rodrigo de Azevedo

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asked Mar 05 '14 at 00:43

user25004

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Just to clarify, the KKT conditions are necessary and sufficient only when some constraint qualifications hold. – S.B. Mar 05 '14 at 01:09
Thanks my statement is not precise. I will fix it now. – user25004 Mar 05 '14 at 01:35
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At least in first order, I think it is true. You can see this resource (Slide #7) for verification. – Nitish Mar 05 '14 at 02:12
That is useful. Thank you Nitish. – user25004 Mar 07 '14 at 16:50
@Nitish What do you mean by "At least in first order"? Isn't the statement in the question simply true? – littleO Nov 10 '17 at 06:05
@littleO First order KKT conditions versus higher order conditions. – user25004 Nov 10 '17 at 20:21

KKT conditions for nonsmooth convex problems

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