Optimization problem, local minima and feasible set

[retspool]

Homework Statement

minimiza f(x) = x_1
subject to (x-1)^2+y^2=1
(x+1)^2+y^2=1

Graph the feasible set, Are there any local minimizers and global minimizers?

Homework Equations

I have graphed the feasible set
http://www.wolframalpha.com/input/?i=graph+%28x-1%29^2%2By^2%3D1+and+%28x%2B1%29^2%2By^2%3D1

The Attempt at a Solution

I don't know if the local minima is going to be (0,0) cause its common to both the constraints or if its going to be some other pt.

thx

 

[lanedance]

what is the function to minimise?
f(x) = x_1

based on the constraints, your feasible set consists of 1 point, so you don't have a whole heap of choices

 

[retspool]

Yeah i was confused cause the 2 constraints met at only one pt. Which made it pretty obvious. I was just confirming that it had only one obvious choice, the origin.

Thx