I write the question $5.29$ in Convex Optimization ,and it said
minimize $-3x_1^2+x_2^2+2x_3^2+2(x_1+x_2+x_3)$
subject to $x_1^2+x_2^2+x_3^2=1$
so strong duality holds even though the problem is not convex
I wonder that if we have to prove it is strong duality and not convex,how should we prove it?