Program in MATLAB a Primal$-$Dual Barrier Method to solve:

minimize $2$ x$\_15$ x$\_2$ subject to:

x$\_1+$ x$\_3=4,$ x$\_2+$ x$\_4=6,$ x$\_1+$ x$\_2+$ x$\_5=8,$

x$\_1,$ x$\_2,$ x$\_3,$ x$\_4,$ x$\_5>=0.$

Use duality gap s$\text{'}$x for tolerance $(1.$e $-4).$ You

may opt for a suitable centering parameter $\backslash$sigma to control barrier parameter $\backslash$mu at each

step. A reference number for $\backslash$sigma is $0\mathrm{.}25.$