Optimization problem, local minima and feasible set

  • #1

Homework Statement

minimiza f(x) = x_1
subject to (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

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.

  • #2
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
  • #3
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.


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