Parametric Sensitivity Analysis (PSA) is a mathematical framework that enables
deterministic local post-optimality analysis of optimisation problems. WORHP uses an SQP method to solve nonlinear optimisation problems. In every outer SQP iteration, WORHP poses a quadratic subproblem to be solved by the internal QP solver. The optimal solutions of these subproblems serve as search direction to determine the next SQP iterates.
Post optimality analysis can be applied to these subproblems in order to improve their
solutions.
The aim of this activity is to implement different algorithms that take profit from the post optimality analysis on the subproblems. WORHP uses Hessian regularisation and constraint relaxation techniques to guarantee the solvability of the subproblems. These quantities are regarded as perturbations. The parametric sensitivities are used to compensate the effects of these perturbations.
Using Taylor series predictions of the QP behaviour with different regularisation and
relaxation values can be computed. Thus, the overall SQP algorithm is improved by
integration of these predictions in order to adjust internal parameters and by calculation of compensating search directions.