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A recently introduced restricted variant of the multidimensional stable roommates problem is the roommate diversity problem: each agent belongs to one of two types (e.g., red and blue), and the agents' preferences over the rooms solely depend on ...

• Popular partitioning on RDP with room size 2 can be computed in polynomial time.
• Mixed popular partitioning is always guaranteed to exist in any RDP instance.
• Deciding if a (strictly) popular partitioning exists is co-NP-hard.
• ...

Accuracy certificates for convex minimization problems allow for online verification of the accuracy of approximate solutions and provide a theoretically valid online stopping criterion. When solving the Lagrange dual problem, accuracy ...

Recently the adaption problem of Information-Based Complexity (IBC) for linear problems in the randomized setting was solved in Heinrich (2024) [8]. Several papers treating further aspects of this problem followed. However, all examples obtained ...

In this paper, we investigate properties of standard and multilevel Monte Carlo methods for weak approximation of solutions of stochastic differential equations (SDEs) driven by infinite-dimensional Wiener process and Poisson random measure with ...

In this paper, we present lower bounds and algorithmic constructions of union-intersection-bounded families of sets. The lower bound is established using the Lovász Local Lemma. This bound matches the best known bound for the size of union-...

Vulnerability identification has been broadly studied as a way to improve cybersecurity. Internet of Things (IoT) ecosystems are considered particularly vulnerable as a whole, due to their widespread deployment, low processing ability, difficulty ...

This paper studies the convergence rate of a second-order dynamical system associated with a nonsmooth bilinearly coupled convex-concave saddle point problem, as well as the convergence rate of its corresponding discretizations. We derive the ...$\left(\mathrm{},,{}^{\mathrm{}}\right)$

This paper is devoted to an octagonal cut algorithm and a hexadecagonal cut algorithm for finding the convex hull of n points in R 2, where some octagon and hexadecagon are used for discarding most of the given points interior to these polygons. ...

We study the non-submodular maximization problem, whose objective function can be expressed as the Difference between two Set (DS) functions or the Ratio between two Set (RS) functions. For the cardinality-constrained and unconstrained DS ...

We present a novel deep-learning method for estimating time-dependent parameters in Markov processes through discrete sampling. Departing from conventional machine learning, our approach reframes parameter approximation as an optimization problem ...

• Novel deep learning application in multivariate regression and SDEs.
• Theoretical support and experimental validation.
• Potential impact across various scientific and engineering fields.

Stochastic first-order methods are standard for training large-scale machine learning models. Random behavior may cause a particular run of an algorithm to result in a highly suboptimal objective value, whereas theoretical guarantees are usually ...

We propose a matrix-free parallel two-level deflation method combined with the Complex Shifted Laplacian Preconditioner (CSLP) for two-dimensional heterogeneous Helmholtz problems encountered in seismic exploration, antennas, and medical imaging. ...

• We introduce a parallel iterative solver for 2D heterogeneous Helmholtz problems with strong and weak scalability.
• A matrix-free parallelization of the two-level deflation method is presented, reducing memory requirements.
• We ...

We study the approximability of the maximum size independent set (MIS) problem in bounded degree graphs. This is one of the most classic and widely studied NP-hard optimization problems. It is known for its inherent hardness of approximation. We ...$\mathrm{}\mathrm{}\mathrm{}$$\mathrm{}$$\mathrm{}\mathrm{}\mathrm{}$

In this paper sharp lower error bounds for numerical methods for jump-diffusion stochastic differential equations (SDEs) with discontinuous drift are proven. The approximation of jump-diffusion SDEs with non-adaptive as well as jump-adapted ...

In this paper we consider finding an approximate second-order stationary point (SOSP) of general nonconvex conic optimization that minimizes a twice differentiable function subject to nonlinear equality constraints and also a convex conic ...$\stackrel{}{\mathcal{}}{}^{\mathrm{}\mathrm{}}$$\stackrel{}{\mathcal{}}{}^{\mathrm{}\mathrm{}}{}^{\mathrm{}\mathrm{}}$$\sqrt{}$$\stackrel{}{\mathcal{}}{}^{\mathrm{}\mathrm{}}$$\stackrel{}{\mathcal{}}{}^{\mathrm{}\mathrm{}}{}^{\mathrm{}\mathrm{}}$

Let t be a positive real number. A graph is called t-tough if the removal of any vertex set S that disconnects the graph leaves at most |S|/t components. The toughness of a graph is the largest t for which the graph is t-tough. We prove that ...$\mathcal{}{}^{\mathrm{}}{}^{\mathrm{}}$$$

In this paper, we propose a new splitting algorithm to find the zero of a monotone inclusion problem that features the sum of three maximal monotone operators and a Lipschitz continuous monotone operator in Hilbert spaces. We prove that the ...

We study rectangle stabbing problems in which we are given n axis-aligned rectangles in the plane that we want to stab, that is, we want to select line segments such that for each given rectangle there is a line segment that intersects two ...$\mathrm{}$$$$$

We study the complexity of randomized computation of integrals depending on a parameter, with integrands from Sobolev spaces. That is, for r , d 1 , d 2 ∈ N, 1 ≤ p , q ≤ ∞, D 1 = [ 0 , 1 ] d 1, and D 2 = [ 0 , 1 ] d 2 we are given f ∈ W p r ( D 1 ...

The convex problem of minimizing $f(\mathbf{x})+g(\mathbf{x})+h(\mathbf{A}\mathbf{x})$ over ${\mathbb{R}}^n$, where f is differentiable and $\mathbf{A}:{\mathbb{R}}^n\to {\mathbb{R}}^m$ is a linear operator, has been extensively studied in the literature. Various algorithms have been proposed from different perspectives, such as ...$\mathrm{}$