Related papers: On Convergence of Discrete Schemes for Computing t…
The article considers the discrete analogue of the method of quickest descent for an inverse Acoustics problem in case of a smooth source. The authors derived the gradient of functional in differential and discrete cases, described the…
This paper deals with the computation of a non-asymptotic lower bound by means of the nonanticipative rate-distortion function (NRDF) on the discrete-time zero-delay variable-rate lossy compression problem for discrete Markov sources with…
We study the compression of data in the case where the useful information is contained in a set rather than a vector, i.e., the ordering of the data points is irrelevant and the number of data points is unknown. Our analysis is based on…
This paper develops a mathematical theory of super-resolution. Broadly speaking, super-resolution is the problem of recovering the fine details of an object---the high end of its spectrum---from coarse scale information only---from samples…
This survey addresses sampling discretization and its connections with other areas of mathematics. The survey concentrates on sampling discretization of norms of elements of finite-dimensional subspaces. We present here known results on…
Optimization problems with continuous data appear in, e.g., robust machine learning, functional data analysis, and variational inference. Here, the target function is given as an integral over a family of (continuously) indexed target…
Many problems in nonlinear analysis and optimization, among them variational inequalities and minimization of convex functions, can be reduced to finding zeros (namely, roots) of set-valued operators. Hence numerous algorithms have been…
This paper concerns a spectral estimation problem in which we want to find a spectral density function that is consistent with estimated second-order statistics. It is an inverse problem admitting multiple solutions, and selection of a…
This paper studies a variant of the rate-distortion problem motivated by task-oriented semantic communication and distributed learning problems, where $M$ correlated sources are independently encoded for a central decoder. The decoder has…
Finite volume methods for problems involving second order operators with full diffusion matrix can be used thanks to the definition of a discrete gradient for piecewise constant functions on unstructured meshes satisfying an orthogonality…
Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these…
The discrete non-commutative Darboux system of equations with self-consistent sources is constructed, utilizing both the vectorial fundamental (binary Darboux) transformation and the method of additional independent variables. Then the…
Discrete optimization belongs to the set of $\mathcal{NP}$-hard problems, spanning fields such as mixed-integer programming and combinatorial optimization. A current standard approach to solving convex discrete optimization problems is the…
Sampling from Gibbs distributions and computing their log-partition function are fundamental tasks in statistics, machine learning, and statistical physics. While efficient algorithms are known for log-concave densities, the worst-case…
In this paper, we propose stochastic structure-preserving schemes to compute the effective diffusivity for particles moving in random flows. We first introduce the motion of particles using the Lagrangian formulation, which is modeled by…
Primal-dual splitting schemes are a class of powerful algorithms that solve complicated monotone inclusions and convex optimization problems that are built from many simpler pieces. They decompose problems that are built from sums, linear…
Time-varying stochastic optimization problems frequently arise in machine learning practice (e.g. gradual domain shift, object tracking, strategic classification). Although most problems are solved in discrete time, the underlying process…
We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…
1) We introduce random discrete Morse theory as a computational scheme to measure the complicatedness of a triangulation. The idea is to try to quantify the frequence of discrete Morse matchings with a certain number of critical cells. Our…
Algorithms for continuous optimization problems have a rich history of design and innovation over the past several decades, in which mathematical analysis of their convergence and complexity properties plays a central role. Besides their…