lambda in fmincon Interior-Point Algorithm with Analytic Hessian

I am trying to use fmincon Interior-Point Algorithm with Analytic Hessian (https://www.mathworks.com/help/optim/ug/fmincon-interior-point-algorithm-with-analytic-hessian.html)

The examplay function is hessinterior which is Hessian of both c(1) and c(2).

My understanding is lambda is Lagrange Multiplier, which should be an output since it is the stationary points of the Lagrangian function. How come it is an input to the function hessinterior?

Thank you very much!

Answer 1

[Matt J]

How come it is an input to the function hessinterior?

Because both x and lambda are computed iteratively. The solver therefore needs to be able to test different choices of Lagrange multipliers.

My understanding is lambda is Lagrange Multiplier, which should be an output

The final lambda is indeed returned as an output.

Answer 2

[Torsten]

My guess is that the algorithm used is a primal-dual algorithm that also iterates the Lagrange multipliers during the solution process.