Related papers: Adapted Sequence for Polyhedral Realization of Cry…
Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years. In this paper, we…
Convex polyhedral abstractions of logic programs have been found very useful in deriving numeric relationships between program arguments in order to prove program properties and in other areas such as termination and complexity analysis. We…
Given a pure, full-dimensional, locally strongly connected polyhedral complex C with convex support, we characterize, by a local codimension-2 condition, polyhedral complexes that coarsen C. The proof of the characterization draws upon a…
A classic problem connecting algebraic and geometric combinatorics is the realization problem: given a poset, determine whether there exists a polytope whose face lattice is the poset. In 1990s, Kapranov defined a poset as a hybrid between…
This paper helps to clarify the status of cylindrical contact homology, a conjectured contact invariant introduced by Eliashberg, Givental, and Hofer in 2000. We explain how heuristic arguments fail to yield a well-defined homological…
We here extend the well known Positive Real Lemma (also known as the Kalman-Yakubovich-Popov Lemma) to complex matrix-valued generalized positive rational function, when non-minimal realizations are considered. We then exploit this result…
We set up a general framework for enriching a subcategory of the category of noncommutative sets over a category C using products of the objects of a non-\Sigma operad P in \C. By viewing the simplicial category as a subcategory of the…
In the early 1990s, a family of combinatorial CW-complexes named permutoassociahedra was introduced by Kapranov, and it was realized by Reiner and Ziegler as a family of convex polytopes. The polytopes in this family are "hybrids" of…
A combinatorial description of the crystal $\mathcal{B}(\infty)$ for finite-dimensional simple Lie algebras in terms of Young tableaux was developed by J. Hong and H. Lee. Using this description, we obtain a combinatorial rule for…
An adaptive regularization strategy for stabilizing Newton-like iterations on a coarse mesh is developed in the context of adaptive finite element methods for nonlinear PDE. Existence, uniqueness and approximation properties are known for…
A convex geometry is finite zero-closed closure system that satisfies the anti-exchange property. Complexity results are given for two open problems related to representations of convex geometries using implication bases. In particular, the…
We present an approach to constrained Horn clause (CHC) verification combining three techniques: abstract interpretation over a domain of convex polyhedra, specialisation of the constraints in CHCs using abstract interpretation of…
In this paper we consider the so-called procedure of {\it Continuous Steiner Symmetrization}, introduced by Brock in \cite{bro95,bro00}. It transforms every domain $\Omega\subset\subset\mathbb{R}^d$ into the ball keeping the volume fixed…
We consider the solution of a stochastic convex optimization problem $\mathbb{E}[f(x;\theta^*,\xi)]$ over a closed and convex set $X$ in a regime where $\theta^*$ is unavailable and $\xi$ is a suitably defined random variable. Instead,…
Many constraints restricting the result of some computations over an integer sequence can be compactly represented by register automata. We improve the propagation of the conjunction of such constraints on the same sequence by synthesising…
This paper is concerned with the relationship between the discrete and the continuous decreasing minimization problem on base-polyhedra. The continuous version (under the name of lexicographically optimal base of a polymatroid) was solved…
Let $(A, I)$ be a bounded prism, and $X$ be a smooth $p$-adic formal scheme over $\Spf(A/I)$. We consider the notion of crystals on Bhatt--Scholze's prismatic site $(X/A)_{\prism}$ of $X$ relative to $A$. We prove that if $X$ is proper over…
We study multivariate tail-dependence compatibility for complete and partial signed tail families, treating lower-tail, upper-tail, and mixed configurations in one geometric witness representation indexed by active coordinate sets and sign…
We develop a theory of bicrystalline ideals, synthesizing Gr\"obner basis techniques and Kashiwara's crystal theory. This provides a unified algebraic, combinatorial, and computational approach that applies to ideals of interest, old and…
This work proposes an implementable proximal-type method for a broad class of optimization problems involving nonsmooth and nonconvex objective and constraint functions. In contrast to existing methods that rely on an ad hoc model…