In these slides (5) the dual function for the norm minimization problem:
$ \min_x \|x\| \quad \mbox{s.t.} \quad Ax =b $
is defined as:
$ g(v) = \inf_x (\|x\| - ν^\intercal Ax + b^\intercal ν) $
what I don't understand is why the signs are reserved. The Lagrangian is according to the same author
$ \|x\| + v^\intercal (Ax - b) $
so the dual function should have been
$ g(v) = \inf_x (\|x\| + ν^\intercal Ax - b^\intercal ν) $
Is this correct?