Karush Kuhn Tucker Optimality Conditions

The Karush–Kuhn–Tucker (KKT) conditions (also known as the Kuhn–Tucker conditions) are first order necessary conditions for a solution in nonlinear programming to be optimal. KKT conditions 3 and 4 are for inequality constraints only and a first case with equality constraints is covered here. The system of equations corresponding to the KKT conditions is usually not solved directly, except in the few special cases (such as this example problem) where a closed-form solution can be derived. This example concludes with a demonstration of how to solve nonlinear problems with a nonlinear programming solver such as APOPT and IPOPT.

[zy]

Thanks for the explanation, very clear clarification on how to use kKT condition to solve equality-constrained objectives

[tanvirkaisar]

thanks for the great explanation. I have a question though, why do we need lagrange multipliers to be positive?

[letztersohndesabendlandes]

No idea if this will get a response, what with this being a five year old video, but I don't see how the example problem is any different than a Lagrange problem. If I just set this up as a Lagrangean, I would get five equations with five unknowns with two of those equations being equal to the constraints. That sets up exactly the same matrix problem as given in the example. I see how KKT is useful when there are inequality constraints, but in this example I don't really see the distinction.

[yogeshsingular]

Can you explain how we get the second set of KKT conditions. Namely that no feasible direction improves the objective? I want to understand the proof

[ArmanAli-wwml]

No one explains the actual meaning of these conditions. For example what does it mean by feasibility here

[Gnsd]

In KKT#2 how did you calculate the constants that are multiplied by each X?

[simonbernard]

"this is a 5min tutorial" -> lasts for 15min

[estebanmoreno]

at 4:40 what if you move everythingto the right side instead of the left i mean, i did that and the signs changed and the answer was different

[masoudsakha]

ٌاWhat about the sufficient conditions?