Korrekturverfahren zur numerischen Lösung nichtlinearer Optimierungsprobleme mittels Methoden der parametrischen Sensitivitätsanalyse

Abstract

The nonlinear optimization has becoming of the key technologies of the field of applied mathematics. There are various numbers of applications in different fields of science, e.g. economics, medicine and engineering. Also industry is using mathematical algorithms for solving nonlinear optimization problems. Especially in the aerospace industry nonlinear optimization is frequently used for optimizing trajectories. The aim of this thesis is to extend an existing method for solving nonlinear optimization problems by using parametric sensitivity analysis. At first the iterative SQP-method WORHP for solving nonlinear optimization problems is described and introduced. Then it is shown that the sensitivity derivatives of a quadratic subproblem within WORHP can be computed efficiently with almost no extra costs. The subproblem is now treated as a perturbed problem. In the thesis several different perturbations are introduced. With the sensitivity derivatives it is now possible to compute an approximation of the solution of the perturbed quadratic subproblem. This solution is used within the overall nonlinear optimization method for obtaining a new iterate. The numerical results show that it is possible to reduce of number of iterations and sometimes it also possible to reduce the time needed for solving a problem.