MATLAB: Should the linear constraints be considered when provide analytic Hessian in fmincon with interior point algorithm

Question

Hi, I am using the fmincon function for optimization, which has both linear and nonlinear constraints. I want to provide the Hessian matrix to improve the efficiency. Based on the examples provided in the documentations, it seems we only need to consider the Hessian matrix corresponding to the Lagrange function that consists of the objective and nonlinear constraints. Does it suggests that we only need to consider the nonlinear constraints in the Hessian for the coding?

While theoretically, based on the optimization, the Lagrange function should include all linear and nonlinear constraints, then the Hessian should be calculated considering all linear and nonlinear constraints.

So, for matlab coding, we only need to consider the objective and nonlinear constraints for the Hessian. Is that right?

Many thanks for the kind help.

Answer 1

The Hessians of linear functions are always zero and therefore linear constraints contribute nothing to the total Hessian of the Lagrangian. That is the reason you are only asked to provide a Hessian calculation for the objective and nonlinear constraint functions.