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In this paper we study the the Gauss image problem, which is a generalization of the Aleksandrov problem in convex geometry. By considering a geometric flow involving Gauss curvature and functions of normal vectors and radial vectors, we…
Large-eddy simulation developments and validations are presented for an improved simulation of turbulent internal flows. Numerical methods are proposed according to two competing criteria: numerical qualities (precision and spectral…
We provide another look at the statistical calibration problem in computer models. This viewpoint is inspired by two overarching practical considerations of computer models: (i) many computer models are inadequate for perfectly modeling…
We study algorithms for the sliding-window model, an important variant of the data-stream model, in which the goal is to compute some function of a fixed-length suffix of the stream. We extend the smooth-histogram framework of Braverman and…
While semidefinite programming (SDP) has traditionally been limited to moderate-sized problems, recent algorithms augmented with matrix sketching techniques have enabled solving larger SDPs. However, these methods achieve scalability at the…
The paper deals with the implicit programming approach to a class of Mathematical Programs with Equilibrium Constraints (MPECs) and bilevel programs in the case when the corresponding reduced problems are solved using a bundle method of…
A large amount of quantitative geospatial data are collected and aggregated in discrete enumeration units (e.g. countries or states). Smooth pycnophylactic interpolation aims to find a smooth, nonnegative function such that the area…
Motivated by the need to better understand the properties of sparse cutting-planes used in mixed integer programming solvers, the paper [2] studied the idealized problem of how well a polytope is approximated by the use of sparse valid…
We propose an adaptive smoothing algorithm based on Nesterov's smoothing technique in \cite{Nesterov2005c} for solving "fully" nonsmooth composite convex optimization problems. Our method combines both Nesterov's accelerated proximal…
We present a method of exploiting symmetries of discrete-time optimal control problems to reduce the dimensionality of dynamic programming iterations. The results are derived for systems with continuous state variables, and can be applied…
Despite the numerous uses of semidefinite programming (SDP) and its universal solvability via interior point methods (IPMs), it is rarely applied to practical large-scale problems. This mainly owes to the computational cost of IPMs that…
Many algorithms for determining properties of real algebraic or semi-algebraic sets rely upon the ability to compute smooth points. Existing methods to compute smooth points on semi-algebraic sets use symbolic quantifier elimination tools.…
Recent works by the second author and Maxwell et al. have shown that the Einstein-scalar field conformal constraint equations are highly complex and generally intractable, even in the vacuum case. In this article, to gain a clearer…
This paper extends the mathematical theory of axisymmetrization and vorticity depletion within the two-dimensional (2D) Euler equations, with an emphasis on the dynamics of radially symmetric, monotonic vorticity profiles. By analyzing…
There has been increasing interest in statistical analysis of data lying in manifolds. This paper generalizes a smoothing spline fitting method to Riemannian manifold data based on the technique of unrolling and unwrapping originally…
For a mean curvature flow of complete graphical hypersurfaces $M_{t}=\operatorname{graph} u(\cdot,t)$ defined over domains $\Omega_{t}$, the enveloping cylinder is $\partial\Omega_{t}\times\mathbb{R}$. We prove the smooth convergence of…
To tackle difficulties for theoretical studies in situations involving nonsmooth functions, we propose a sequence of infinitely differentiable functions to approximate the nonsmooth function under consideration. A rate of approximation is…
We propose a variational regularization approach based on a multiscale representation called cylindrical shearlets aimed at dynamic imaging problems, especially dynamic tomography. The intuitive idea of our approach is to integrate a…
Polytopes are the basic finite data structures for convex sets: they appear as feasible regions in linear optimization, as geometric summaries in algorithms, and as random objects in stochastic geometry. A natural geometric question is…
This work presents two novel approaches for the symplectic model reduction of high-dimensional Hamiltonian systems using data-driven quadratic manifolds. Classical symplectic model reduction approaches employ linear symplectic subspaces for…