# A Certain convex minimization problem

1. May 22, 2016

### nikozm

Hi, I would like to know if the inequality sign plays any role to the following optimization problem:

minimize f0(x)
subject to f1(x)>=0

where both f0(x) and f1(x) are convex. The standard form of these problems require a constraint such as: f1(x)<=0, but i am interested in the opposite condition (f1(x)>=0) and solving it using the standard Lagrangian method and KKT conditions. Is this right?

Any help would be useful. Thanks in advance!

2. May 27, 2016

### Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

3. May 28, 2016

### Office_Shredder

Staff Emeritus
The method essentially says that the solution occurs when the inequality is strict, and you can just find points where the gradient is zero, or the inequality is an equality, and you can use Lagrangian multipliers. It doesn't matter whether the inequality is less than or greater than, everything I said above still holds.

4. Jun 3, 2016

### sargondjani1

f1(x)>=0 is the same as -f1(x)<=0, so just define f1 appropriately and you get the 'normal' KKT conditions.