arXiv subjects

Jan Kuratko

Publications and source records attributed to Jan Kuratko.

2 recordsLinked to original sources

arXiv2017

Solving Reachability Problems by a Scalable Constrained Optimization Method

In this paper we consider the problem of finding an evolution of a dynamical system that originates and terminates in given sets of states. However, if such an evolution exists then it is usually not unique. We investigate this problem and find a scalable approach for solving it. To this end we formulate an equality constrained nonlinear program that addresses the non-uniqueness of the solution of the original problem. In addition, the resulting saddle-point matrix is sparse. We exploit the structure in order to reach an efficient implementation of our method. In computational experiments we compare line search and trust-region methods as well as various updates for the Hessian.

math.OC↗

arXiv2016

Solving Underdetermined Boundary Value Problems By Sequential Quadratic Programming

Ordinary differential equations that model technical systems often contain states, that are considered dangerous for the system. A trajectory that reaches such a state usually indicates a flaw in the design. In this paper, we present and study the properties of an algorithm for finding such trajectories. That is, for a given ordinary differential equation, the algorithm finds a trajectory that originates in one set of states and reaches another one. The algorithm is based on sequential quadratic programming applied to a regularized optimization problem obtained by multiple shooting.

math.OC↗