A Structure Utilizing Inexact Primal-Dual Interior-Point Method for Analysis of Linear Differential Inclusions

The ability to analyze system properties for large scale systems is an important part of modern engineering. Although computer power increases constantly, there is still need to develop tailored methods that are able to handle large scale systems, since sometimes standard methods cannot handle the large scale problems that occur. In this thesis the focus is on system analysis, in particular analysis methods that result in optimization problems with a specific problem structure. In order to solve these optimization problems, primal-dual interior-point methods have been tailored to the specific structure. A convergence proof for the suggested algorithm is also presented. It is the structure utilization and the use of an iterative solver for the search directions that enables the algorithm to be applied to optimization problems with a large number of variables. However, the use of an iterative solver to find the search directions will give infeasible iterates in the optimization algorithm. This make the use of an infeasible method desirable and hence is such a method proposed. Using an iterative solver requires a good preconditioner. In this work two different preconditioners are used for different stages of the algorithm. The first preconditioner is used in the initial stage, while the second preconditioner is applied when the iterates of the algorithm are close to the boundary of the feasible set. The proposed algorithm is evaluated in a simulation study. It is shown that problems which are unsolvable for a standard solver are solved by the proposed algorithm.