I need $5\mathrm{.}4$ answer, thank you! 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 $1^{TT}(1+c{)}^{+}=1.$

Exercise $5\mathrm{.}3$ Let $c,din{R}^n.$ Assume $d>0$ and $D=(Diag(d)).$ Show that the

solution to

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

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

$,x0$

Quadratic Programming: Theory and Algorithms

is

$x=(d+Dc{)}^{+},$

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

Exercise $5\mathrm{.}4$ Write a CVX MATLAB script that takes as inputs $cin{R}^n,$Qin

$R^{nn},Ain{R}^{mn},bin{R}^m$ and solves the optimization problem

min,$\frac{1}{2}{x}^{TT}Qx+c^{TT}x$

$s.t.Ax=b$

$,x0.$

Test your script on instances generated as follows:andAre the results consistent with Exercises $5\mathrm{.}2$ and $5\mathrm{.}3?$I I