Exercise $5\mathrm{.}2$ Let $cin{R}^n.$ Show that the solution to

$mi{n}_x,\frac{1}{2}||x|{|}_2^2-c^{TT}x$

$s.t.1^{TT}x=1$

$,x0$

is

$x=(1+c{)}^{+},$

where $inR$ is a suitable threshold value such that $1^{TT}(1+c{)}^{+}=1.$