(a) One way to formulate the projection problem is $$\min \frac{1}{2}\|x-a\|^2$$ $$s.t \> Ax=0$$ where $A$ is a matrix such that $L = \{x : Ax = 0\}$
(i) Formulate the Lagrange dual $(D _1 )$ of $ (P _1 )$, and prove whether strong duality between $(P _1 )$ and $(D_1 )$ holds.
Write down Lagrangian problem using Lagrange multipliers $L(x,v)=\frac{1}{2}\|x-a\|^2+<Ax,v>$ Find Lagrange dual function $\inf_{x}L(x,v)=\inf_{x}\{\frac{1}{2}\|x-a\|^2+<Ax,v>\}=\inf_{x}\{\frac{1}{2}<x-a,x-a>+<v,Ax>\}$ Find the Lagrange dual function
So I think I’m not understanding how to simply the above expression to