understanding how the SQP optimization method works

Dear ALl

i am trying to understand how the SQP approaching optimum solution. generaly, SQP is not forcing feasibility at each itration. that means that sometimes, solution may not be satisfying the constraint.

however, according to the Wikipedia explaination of the SQP https://optimization.mccormick.northwestern.edu/index.php/Sequential_quadratic_programming

the SQP solving the lagrangian equation that is formed by the deriaivatives of the KKT function. since the KKT function containes thress terms. one for objective function and one for equality constraints and one for inequality constraints, that means that SQP minimizes the objective function and constraints together. and whenever it converges, the proposed solution is feasible. and that contrast the first scentance i mentioned here.

what do you think?

Thank You in advance

Answer 1

[Alan Weiss]

The fmincon sqp algorithm is described here, with some tweaks explained here. Perhaps this will provide some help, or at least pointers to more extensive explanations.

Alan Weiss

MATLAB mathematical toolbox documentation