Lagrange Multiplier method (Lagrange Multiplier) and Kkt conditions

Lagrange Multiplier method: For the optimization problem of equality constraint, the optimal value is obtained.

Kkt condition: The optimal value is obtained for the optimization problem with inequality constraints.

Optimization Problem Classification:

(1) Unconstrained optimization problem:

The Fermat theorem is often used, that is, the derivative is obtained, and then it is zero, and the candidate optimal value can be obtained.

(2) An optimization problem with equality constraints:

Using the Lagrange multiplier method, the equation constraint is written as a formula with a coefficient called the Lagrangian function. The optimal value is obtained by the derivative of each parameter and the conforming type.

(3) An optimization problem with inequality constraints. ，，.

All inequality constraints, equality constraints, and objective functions are all written as an equation:.

The optimal value of the KKT condition must meet the following conditions:

1, the derivative is zero;

2.

3,.

Lagrange Multiplier method (Lagrange Multiplier) and Kkt conditions