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What are the Karush–Kuhn–Tucker conditions for $\min_x \frac{1}{2} ||x-u||_2^2:$ subject to $||x||_1\le c$

Apparently these are the conditions enter image description here

but it's not all that clear how this can be applied to above function, especially the stationarity portion.

WetlabStudent
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user8714896
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    Be sure to specify whether this is a homework problem for a class. You might get more answers on math.stackexchange as this is only tangentially related to stats. – WetlabStudent Nov 29 '20 at 20:34
  • @WetlabStudent yes it's for a class. I don't normally post these kind of questions on Math stack exchange cause whenever I post something stats related it tends to get avoided and never receives answers for whatever reason, but when posted on here someone seems to be familiar with the concepts and provides an answer. – user8714896 Nov 29 '20 at 22:42
  • I've marked it self-study so folks know to give "helpful hints" rather than complete answers. – WetlabStudent Nov 29 '20 at 23:37
  • I would translate one norm into two constraints $-c0$ then constraint is binding: Can both constraints be binding? When will one constraint be binding? When will none be binding? – Jesper for President Nov 30 '20 at 03:06

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