Related papers: Optimal interpolation with spatial rational Pythag…
We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the…
In this paper, we give a causal solution to the problem of spline interpolation using H-infinity optimal approximation. Generally speaking, spline interpolation requires filtering the whole sampled data, the past and the future, to…
In the space of holomorphic functions in a convex domain it is studied the interpolation problem by means of sums of the series of exponentials converging uniformly on all compact sets of the domain. The discrete set of the interpolation…
Cubic spline interpolation on Euclidean space is a standard topic in numerical analysis, with countless applications in science and technology. In several emerging fields, for example computer vision and quantum control, there is a growing…
Optimal model reduction for large-scale linear dynamical systems is studied. In contrast to most existing works, the systems under consideration are not required to be stable, neither in discrete nor in continuous time. As a consequence,…
On the space of probability densities, we extend the Wasserstein geodesics to the case of higher-order interpolation such as cubic spline interpolation. After presenting the natural extension of cubic splines to the Wasserstein space, we…
In this paper, we consider optimization problems w.r.t. to pairs of orthogonal matrices $XY = I$. Problems of this form arise in several applications such as finding shape correspondence in computer graphics. We show that the space of such…
A realistic generalization of the Markov--Dubins problem, which is concerned with finding the shortest planar curve of constrained curvature joining two points with prescribed tangents, is the requirement that the curve passes through a…
Convex optimization encompasses a wide range of optimization problems that contain many efficiently solvable subclasses. Interior point methods are currently the state-of-the-art approach for solving such problems, particularly effective…
Most of the optimal guidance problems can be formulated as nonconvex optimization problems, which can be solved indirectly by relaxation, convexification, or linearization. Although these methods are guaranteed to converge to the global…
We present a general (i.e., independent of the underlying model) interpolation technique based on optimal transportation of Gaussian models for parametric advection-dominated problems. The approach relies on a scalar testing function to…
A method is devised for numerically solving a class of finite-horizon optimal control problems subject to cascade linear discrete-time dynamics. It is assumed that the linear state and input inequality constraints, and the quadratic measure…
In this paper, we study the optimal transport problem induced by separable cost functions. In this framework, transportation can be expressed as the composition of two lower-dimensional movements. Through this reformulation, we prove that…
This paper is devoted to a study of infinite horizon optimal control problems with time discounting and time averaging criteria in discrete time. We establish that these problems are related to certain infinite-dimensional linear…
We present a new method for the interpolation of given data points and associated normals with surface parametric patches with rational normal fields. We give some arguments why a dual approach is the most convenient for these surfaces,…
In this paper, we study unirational differential curves and the corresponding differential rational parametrizations. We first investigate basic properties of proper differential rational parametrizations for unirational differential…
This article focuses on numerical efficiency of projection algorithms for solving linear optimization problems. The theoretical foundation for this approach is provided by the basic result that bounded finite dimensional linear optimization…
We consider algorithmic approaches to the D-optimality problem for cases where the input design matrix is large and highly structured, in particular implicitly specified as a full quadratic or linear response-surface model in several levels…
Decomposition techniques for linear programming are difficult to extend to conic optimization problems with general non-polyhedral convex cones because the conic inequalities introduce an additional nonlinear coupling between the variables.…
In the past few decades polynomial curves with Pythagorean Hodograph (for short PH curves) have received considerable attention due to their usefulness in various CAD/CAM areas, manufacturing, numerical control machining and robotics. This…