Question: Linear programming problems about norms in compressed sensing. Thank you in advance! Exercise 4. In compressed sensing, one wishes to solve problems of the type

Linear programming problems about norms in compressed sensing. Thank you in advance!

Exercise 4. In compressed sensing, one wishes to solve problems of the type min lello s.t. An: = b where :c E R", and ||$||0 = #{z' : 1c, 34$ 0}, that is, the number of nonzero entries of :15. Show the following: ' H ' \"0 is not a convex function, i.e., there exist :5, y E R\" and A E [0,1] such that \"M? + (1 - Myllo i Allxllo + (1 - Mllyllo- 0 || . \"1 is a convex function

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