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We present a method of solving the T-optimal design problem for nonlinear dynamical systems using dynamic programming. In contrast with previous dynamic programming formulations, we avoid adding an equation for the dispersion to the system…
The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…
In this paper, we extend the dynamical low-rank approximation method to the space of finite signed measures. Under this framework, we derive stochastic low-rank dynamics for stochastic differential equations (SDEs) coming from classical…
Dynamic optimization problems involving discrete decisions have several applications, yet lead to challenging optimization problems that must be addressed efficiently. Combining discrete variables with potentially nonlinear constraints…
A recently developed method for the calculation of Lyapunov exponents of dynamical systems is described. The method is applicable whenever the linearized dynamics is Hamiltonian. By utilizing the exponential representation of symplectic…
Lifting methods allow to transform hard variational problems such as segmentation and optical flow estimation into convex problems in a suitable higher-dimensional space. The lifted models can then be efficiently solved to a global optimum,…
The symplectic Stiefel manifold, denoted by $\mathrm{Sp}(2p,2n)$, is the set of linear symplectic maps between the standard symplectic spaces $\mathbb{R}^{2p}$ and $\mathbb{R}^{2n}$. When $p=n$, it reduces to the well-known set of $2n\times…
This study focuses on using direct methods (first-discretize-then-optimize) to solve optimal control problems for a class of nonsmooth dynamical systems governed by differential variational inequalities (DVI), called optimal control…
We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…
In this work, we develop a new framework for dynamic network flow problems based on optimal transport theory. We show that the dynamic multi-commodity minimum-cost network flow problem can be formulated as a multi-marginal optimal transport…
In this paper, we consider the problem of solving a constrained system of nonlinear equations. We propose an algorithm based on a combination of the Newton and conditional gradient methods, and establish its local convergence analysis. Our…
First of all, this paper presents some improvements of DSMC method in the form of new schemes and approaches, that, for a wide class of problems, increase performance and reduce the demands on computer resources. The most important…
A damped Newton's method to find a singularity of a vector field in Riemannian setting is presented with global convergence study. It is ensured that the sequence generated by the proposed method reduces to a sequence generated by the…
This paper focus on investigating the distributed Riemannian stochastic optimization problem on the Stiefel manifold for multi-agent systems, where all the agents work collaboratively to optimize a function modeled by the average of their…
We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…
Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…
Matched pairs of Lie groupoids and Lie algebroids are studied. Discrete Euler-Lagrange equations are written for the matched pairs of Lie groupoids. As such, a geometric framework to analyse a discrete system by decomposing it into two…
The paper presents a dynamic solution method for dynamic minimum parametric networks flow. The solution method solves the problem for a special parametric dynamic network with linear lower bound functions of a single parameter. Instead…
We study semidefinite programming (SDP) relaxations for the NP-hard problem of globally optimizing a quadratic function over the Stiefel manifold. We introduce a strengthened relaxation based on two recent ideas in the literature: (i) a…
A discrete time control algorithm using the damped least squares is introduced for acceleration and energy exchange controls in nonlinear vibrating systems. It is shown that the damping constant of least squares and sampling time step of…