**KKT conditions** are derivative tests of the first order for optimal solutions. These solutions are contained within a

Before we go ahead and explain the KKT theorem, it is necessary to understand what a saddle point is.

Let's look at the graph below:

You will notice that the point

The **KKT theorem** is simple. Let's say we choose a variable from the convex subset of these three values —** **of the Lagrangian function, then

The KKT theorem makes use of the

Note:Read more about hyperplane theorems here.

Now, let's go forward and look at the conditions of the KKT theorem.

There are exactly four conditions for the problem defined in the KKT theorem:

**Stationarity condition**(inequality + equality constraint)**Complementary slackness**(assurance of no feasible direction that could improve the function)**Primal feasibility**(inequality constraint)**Dual feasibility**(inequality constraint)

The problem we stated above is one subjected to minimization. For our explanation, let's suppose a problem

Let's now state the conditions of this problem

The stationarity condition tends to take a

This dual pair tends to minimize the

This condition is only defined for inequality constraints:

In the statement given above, either the variable

Primal feasibility basically means that the "subject to" conditions defined in the problem

The dual feasibility condition states that the dual variables must be non-negative:

Once all of these conditions are fulfilled, we can assume that we've found the optimal solution

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