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Second-order optimality conditions of the bilevel programming problems are dependent on the second-order directional derivatives of the value functions or the solution mappings of the lower level problems under some regular conditions,…

We consider vector and set optimization problems with respect to variable domination structures given by set-valued mappings acting between the preimage space and the image space of the objective mapping, as well as by set-valued mappings…

Axiomatizing covarieties of coalgebras for an endofunctor is less intuitive than axiomatizing varieties of algebras via equations (Dahlqvist and Schmid, 2022). Existing techniques come from coalgebraic modal logic, pattern avoidance…

Many high-dimensional optimisation problems exhibit rich geometric structures in their set of minimisers, often forming smooth manifolds due to over-parametrisation or symmetries. When this structure is known, at least locally, it can be…

Polynomial reduction is one of the main tools in computational algebra with innumerable applications in many areas, both pure and applied. Since many years both the theory and an efficient design of the related algorithm have been solidly…

It is known that the set of all solutions of a commutant lifting and other interpolation problems admits a Redheffer linear-fractional parametrization. The method of unitary coupling identifies solutions of the lifting problem with minimal…

We derive computationally tractable formulations of the robust counterparts of convex quadratic and conic quadratic constraints that are concave in matrix-valued uncertain parameters. We do this for a broad range of uncertainty sets. In…

Coherence theorems for covariant structures carried by a category have traditionally relied on the underlying term rewriting system of the structure being terminating and confluent. While this holds in a variety of cases, it is not a…

Traditional methods for covariate adjustment of treatment means in designed experiments are inherently conditional on the observed covariate values. In order to develop a coherent general methodology for analysis of covariance, we propose a…

A novel algorithm for designing optimized orthonormal transform-matrix codebooks for adaptive transform coding of a non-stationary vector process is proposed. This algorithm relies on a block-wise stationary model of a non-stationary…

Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary…

We define sets of orthogonal polynomials satisfying the additional constraint of a vanishing average. These are of interest, for example, for the study of the Hohenberg-Kohn functional for electronic or nucleonic densities and for the study…

A binarization of a bounded variable $x$ is a linear formulation with variables $x$ and additional binary variables $y_1,\dots, y_k$, so that integrality of $x$ is implied by the integrality of $y_1,\dots, y_k$. A binary extended…

This article aims to explore the bridge between the algebraic structure of a linear code and the complete decoding process. To this end, we associate a specific binomial ideal $I_+(\mathcal C)$ to an arbitrary linear code. The binomials…

We provide a correspondence between one-sided coideal subrings and one-sided ideal two-sided coideals in an arbitrary bialgebroid. We prove that, under some expected additional conditions, this correspondence becomes bijective for Hopf…

Covering and elimination inequalities are central to combinatorial optimization, yet their role has largely been studied in problem-specific settings or via no-good cuts. This paper introduces a unified perspective that treats these…

In this work we study the polytope associated with a 0,1-integer programming formulation for the Equitable Coloring Problem. We find several families of valid inequalities and derive sufficient conditions in order to be facet-defining…

We study the set covering polyhedron related to circulant matrices. In particular, our goal is to characterize the first Chv\'atal closure of the usual fractional relaxation. We present a family of valid inequalities that generalizes the…

An algorithm is presented that generates sets of size equal to the degree of a given variety defined by a homogeneous ideal. This algorithm suggests a versatile framework to study various problems in combinatorial algebraic geometry and…

Neural networks have become ubiquitous tools for solving signal and image processing problems, and they often outperform standard approaches. Nevertheless, training neural networks is a challenging task in many applications. The prevalent…