In this paper the abstract of the thesis ”New Interior Point Algorithms in Linear Programming” is presented. The purpose of the thesis is to elaborate new interior point algorithms for solving linear optimization problems. The theoretical complexity of the new algorithms are calculated. We also prove that these algorithms are polynomial. The thesis is composed of seven chapters. In the first ch...

We present a predictor{corrector non{interior path following algorithm for the monotone linear complementarity problem based on Chen{Harker{Kanzow{Smale smoothing techniques. Although the method is modeled on the interior point predictor{ corrector strategies, it is the rst instance of a non{interior point predictor{corrector algorithm. The algorithm is shown to be both globally linearly conver...

We give an algorithm to compute a (Euclidean) shortest path in a polygon with h holes and a total of n vertices. The algorithm uses O(n) space and requires O(n + h 2 log n) time.

Primal-dual path-following algorithms are considered for determinant maximization problem (maxdet-problem). These algorithms apply Newton's method to a primal-dual central path equation similar to that in semideenite programming (SDP) to obtain a Newton system which is then symmetrized to avoid nonsymmetric search direction. Computational aspects of the algorithms are discussed, including Mehro...

A neural-network based approach to the control of non-linear dynamical systems such as wheeled mobile robots is presented. A general framework for the training of neural controllers is outlined, and applied to the lateral control of a vehicle for the path following and trajectory servoing problems. Simulation as well as experimental results on a four-wheel drive vehicle equipped with actuators ...

Algorithmically, many machine learning tasks boil down to solving parameterized optimization problems. The choice of the parameter values in these problems can have a significant influence on the statistical performance of the corresponding methods. Thus, algorithmic support for choosing good parameter values has received quite some attention recently, especially algorithms for computing the wh...

In this paper we present an approximation algorithm for solving the following optimal motion planning problem: Given a planar space composed of triangular regions , each of which is associated with a positive unit weight, and two points s and t, nd a path from s to t with the minimum weight, where the weight of a path is deened to be the weighted sum of the lengths of the sub-paths within each ...

We consider the following natural “above guarantee” parameterization of the classical Longest Path problem: For given vertices s and t of a graph G, and an integer k, the problem Longest Detour asks for an (s, t)-path in G that is at least k longer than a shortest (s, t)-path. Using insights into structural graph theory, we prove that Longest Detour is fixed-parameter tractable (FPT) on undirec...