Related papers: Maximal lattice-free convex sets in linear subspac…
Two lattice points are visible to one another if there exist no other lattice points on the line segment connecting them. In this paper we study convex lattice polygons that contain a lattice point such that all other lattice points in the…
We study a specific convex maximization problem in n-dimensional space. The conjectured solution is proved to be a vertex of the polyhedral feasible region, but only a partial proof of local maximality is known. Integer sequences with…
Monotone linear relations play important roles in variational inequality problems and quadratic optimizations. In this paper, we give explicit maximally monotone linear subspace extensions of a monotone linear relation in finite dimensional…
The purpose of this paper is to study convex bodies $C$ for which there exists no convex body $C^\prime\subsetneq C$ of the same lattice width. Such bodies shall be called ``lattice reduced'', and they occur naturally in the study of the…
We deal with equations over free semilattice of infinite rank and prove that any infinite consistent system of equations is equivalent to its finite subsystem. Moreover, we describe irreducible algebraic sets and solve some algorithmic…
Recently, cutting planes derived from maximal lattice-free convex sets have been studied intensively by the integer programming community. An important question in this research area has been to decide whether the closures associated with…
This paper concerns parameterized convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional Banach (resp. finite-dimensional) spaces and that are indexed by an arbitrary fixed set T…
Convex geometry has recently attracted great attention as a framework to formulate general probabilistic theories. In this framework, convex sets and affine maps represent the state spaces of physical systems and the possible dynamics,…
All known examples of homogeneous Einstein metrics of negative Ricci curvature can be realized as left-invariant Riemannian metrics on solvable Lie groups. After defining a notion of maximal symmetry among left-invariant Riemannian metrics…
Given any finite set of nonnegative integers, there exists a closed convex set whose facial dimension signature coincides with this set of integers, that is, the dimensions of its nonempty faces comprise exactly this set of integers. In…
This work is concerned with the formulation of a general framework for the analysis of meshfree approximation schemes and with the convergence analysis of the Local Maximum-Entropy (LME) scheme as a particular example. We provide conditions…
We show that a free vector lattice over a real vector space $V$ can be realised canonically as a vector lattice of real-valued positively homogeneous functions on any linear subspace of its dual space that separates the points of $V$. This…
Let $G$ be a subgroup of $\mathrm{SL}(\mathbb{R}^{d+1})\ltimes\mathbb{R}^{d+1}$ obtained by adding a translation part to a torsion-free discrete subgroup of $\mathrm{SL}(\mathbb{R}^{d+1})$ dividing a convex cone in the sense of Benoist. We…
For any non-trivial convex and bounded subset $C$ of a Banach space, we show that outside of a $\sigma$-porous subset of the space of non-expansive mappings $C\to C$, all mappings have the maximal Lipschitz constant one witnessed locally at…
In mathematical modelling, the data and solutions are represented as measurable functions and their quality is oftentimes captured by the membership to a certain function space. One of the core questions for an analysis of a model is the…
Farkas' lemma for semidefinite programming characterizes semidefinite feasibility of linear matrix pencils in terms of an alternative spectrahedron. In the well-studied special case of linear programming, a theorem by Gleeson and Ryan…
The positive existential theories of the sets $M_n(\mathbb N)$ without parameters build an inclusion lattice isomorhic with the lattice of divisibility. All these sets are algorithmically undecidable. In further sections some easier…
It was shown by Nachbin in 1950 that an $n$-dimensional normed space $X$ is injective or equivalently is an absolute 1-Lipschitz retract if and only if $X$ is linearly isometric to $l_\infty^n$ (i.e., $\mathbb{R}^n$ endowed with the…
In pure integer linear programming it is often desirable to work with polyhedra that are full-dimensional, and it is well known that it is possible to reduce any polyhedron to a full-dimensional one in polynomial time. More precisely, using…
We prove that if $M$ is an infinite complete metric space then the set of strongly norm-attaining Lipschitz functions $\SA(M)$ contains a linear subspace isomorphic to $c_0$. This solves an open question posed by V. Kadets and O. Rold\'an.