I was just presented with this in Optimization class involving an optimization problem, on which I have no clue, it reads:
(P) minimize-> $ f(x_1,x_2) = (x_1^2 -2x_1 + x_2^2 + 1)^{1/2} $ subject to $ g(x_1,x_2) = x_1+x_2 \leq 0 $
The problem asks us to compute the function $ MP(z) $ meaning the solution to the problem :
(P) minimize-> $ f(x_1,x_2) = (x_1^2 -2x_1 + x_2^2 + 1)^{1/2} $ subject to $ g(x_1,x_2) = x_1+x_2 \leq z $
as a function of z. I have noticed that the goal function f is a square root so it is not a convex program so Karush-Kuhn-Tucker as I studied it is inapplicable here, so my only other option that is from my arsenal is using the penalty method but that seems too intricate for the specific f here. Is there anything I can try besides Karush-Kuhn-Tucker or the penalty functions method? Help appreciated