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We study minimization of a structured objective function, being the sum of a smooth function and a composition of a weakly convex function with a linear operator. Applications include image reconstruction problems with regularizers that…
This paper considers the problem of minimizing the ordered weighted average (or ordered median) function of finitely many rational functions over compact semi-algebraic sets. Ordered weighted averages of rational functions are not, in…
This paper revisits a fundamental problem in statistical inference from a non-asymptotic theoretical viewpoint $\unicode{x2013}$ the construction of confidence sets. We establish a finite-sample bound for the estimator, characterizing its…
The Wendland functions are a class of compactly supported radial basis functions with a user-specified smoothness parameter. We prove that with a linear change of variables, both the original and the "missing" Wendland functions converge…
In this paper, we study functions of bounded variation on a complete and connected metric space with finite one-dimensional Hausdorff measure. The definition of BV functions on a compact interval based on pointwise variation is extended to…
Ordinary differential equations (ODEs) are used to model dynamic systems appearing in engineering, physics, biomedical sciences and many other fields. These equations contain unknown parameters, say $\theta$ of physical significance which…
In the settings of Euclidean Jordan algebras, normal decomposition systems (or Eaton triples), and structures induced by complete isometric hyperbolic polynomials, we consider the problem of optimizing a certain combination (such as the…
Numerical solutions of differential equations are usually not smooth functions. However, they should resemble the smoothness of the corresponding real solutions in one way or another. In two of our recent papers, a kind of spacial…
The (delta-) normal cone to an arbitrary intersection of sublevel sets of proper, lower semicontinuous, and convex functions is characterized, using either epsilon-subdifferentials at the nominal point or exact subdifferentials at nearby…
A waveguide G lies in the (n+1)-dimensional Euclidean space for positive integer n, and outside a large ball coincides with the union of finitely many non-overlapping semi-cylinders ("cylindrical ends"). The waveguide is described by the…
This paper discusses a general and useful stability principle which, roughly speaking, says that given a uniformly continuous function defined on an arbitrary metric space, if the function is bounded on the constraint set and we slightly…
In the paper, properties of orbit functions are reviewed and further developed. Orbit functions on the Euclidean space $E_n$ are symmetrized exponential functions. The symmetrization is fulfilled by a Weyl group corresponding to a…
In this note we introduce and solve a soft classification version of the famous Bayesian sequential testing problem for a Brownian motion's drift. We establish that the value function is the unique non-trivial solution to a free boundary…
Gradient matching with Gaussian processes is a promising tool for learning parameters of ordinary differential equations (ODE's). The essence of gradient matching is to model the prior over state variables as a Gaussian process which…
A nonuniform Neumann boundary-value problem is considered for the Poisson equation in a thin domain $\Omega_\varepsilon$ coinciding with two thin rectangles connected through a joint of diameter ${\cal O}(\varepsilon)$. A rigorous procedure…
Two numerical algorithms are proposed for computing an interval matrix containing the matrix gamma function. In 2014, the author presented algorithms for enclosing all the eigenvalues and basis of invariant subspaces of $A \in \mathbb{C}^{n…
The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…
In metric measure spaces, we study boundary traces of BV functions in domains equipped with a doubling measure and supporting a Poincar\'e inequality, but possibly having a very large and irregular boundary. We show that the trace exists in…
In Bayesian machine learning, the posterior distribution is typically computationally intractable, hence variational inference is often required. In this approach, an evidence lower bound on the log likelihood of data is maximized during…
In this paper we extend classical criteria for determining lower bounds for the least point of the essential spectrum of second-order elliptic differential operators on domains $\Omega\subset\R^n$ allowing for degeneracy of the coefficients…