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We present a method for solving general nonconvex-strongly-convex bilevel optimization problems. Our method -- the \emph{Restarted Accelerated HyperGradient Descent} (\texttt{RAHGD}) method -- finds an $\epsilon$-first-order stationary…
We introduce a class of specially structured linear programming (LP) problems, which has favorable modeling capability for important application problems in different areas such as optimal transport, discrete tomography and economics. To…
Non-Hermitian rotation-time reversal (RT)-symmetric spin models possess two distinct phases, the unbroken phase in which the entire spectrum is real and the broken phase which contains complex eigenspectra, thereby indicating a transition…
Dynamic target detection and target tracking are hot issues in the field of image. In order to explore its application value in the field of mobile robot, a dynamic target detection and tracking system is designed based on hexapod robot.…
A topological approach and understanding to the detection of unstable periodic orbits based on a recently proposed method (PRL 78, 4733 (1997)) is developed. This approach provides a classification of the set of transformations necessary…
The motion of point vortices constitutes an especially simple class of solutions to Euler's equation for two dimensional, inviscid, incompressible, and irrotational fluids. In addition to their intrinsic mathematical importance, these…
The homotopy continuation method has been widely used in solving parametric systems of nonlinear equations. But it can be very expensive and inefficient due to singularities during the tracking even though both start and end points are…
We develop arbitrarily high-order, stationarity-preserving stabilized finite element methods for multidimensional nonlinear hyperbolic balance laws on Cartesian grids. We aim at approximating all the steady states of the problem at hand,…
We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the…
This paper presents a novel feedback method on the motion planning for unicycle robots in environments with static obstacles, along with an extension to the distributed planning and coordination in multi-robot systems. The method employs a…
We provide analytic solutions of the nonlinear differential equation system describing the particle paths below small-amplitude periodic gravity waves travelling on a constant vorticity current. We show that these paths are not closed…
We introduce a new class of Runge-Kutta type methods suitable for time stepping to propagate hyperbolic solutions within tent-shaped spacetime regions. Unlike standard Runge-Kutta methods, the new methods yield expected convergence…
High-index saddle dynamics (HiSD) is an effective approach for computing saddle points of a prescribed Morse index and constructing solution landscapes for complex nonlinear systems. However, for problems with ill-conditioned Hessians…
Many entropy-conservative and entropy-stable (summarized as entropy-preserving) methods for hyperbolic conservation laws rely on Tadmor's theory for two-point entropy-preserving numerical fluxes and its higher-order extension via flux…
In the High-Level Trigger (HLT) of both electron-positron and hadron collision experiments, the tracking process for large-volume gaseous detectors typically consumes a latency of hundreds of milliseconds. Upgrades of existing experiments…
We consider dynamical systems evolving near an equilibrium statistical state where the interest is in modelling long term behavior that is consistent with thermodynamic constraints. We adjust the distribution using an entropy-optimizing…
We introduce new machine-learning techniques for analyzing chaotic dynamical systems. The primary objectives of the study include the development of a new and simple method for calculating the Lyapunov exponent using only two trajectory…
We present a theoretical investigation of wave dynamics in two-dimensional non-Hermitian $\mathcal{PT}$-symmetric lattices, where onsite, as well as inter-site control couplings are employed. Our analysis shows that these couplings can be…
This paper proposes a data-driven motion-planning framework for nonlinear systems that constructs a sequence of overlapping invariant polytopes. Around each randomly sampled waypoint, the algorithm identifies a convex admissible region and…
We study dynamic algorithms in the model of algorithms with predictions. We assume the algorithm is given imperfect predictions regarding future updates, and we ask how such predictions can be used to improve the running time. This can be…