Skip to content

Constrained and unconstrained optimization

19/08/2011
  • Unconstrained optimization:
min f(x)

For unconstrianted optimization, a necessary condition is \nabla f(x)=0.

The interpretion is: if \nabla f(x)\ne 0, f(x) can be still reduced if x moves along -\nabla f(x).

  • Constrained optimization:
min f(x)
subject to h(x)=0

For unconstrianted optimization, a necessary condition is \nabla f(x)=\lambda \nabla h(x).

The interpretion is: project \nabla f(x) to the tangent plane of h(x)=0. Move x along with the projection, f(x) can be reduced.

Keep in mind that: the gradient \nabla f(x) plays a very important role in optimization.

Advertisements
No comments yet

Leave a Reply

Please log in using one of these methods to post your comment:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: