Tootfinder

A polynomial projective algorithm for convex feasibility problems with positive-definite constraints
Sergei Chubanov
https://arxiv.org/abs/2506.15484 https…

A polynomial projective algorithm for convex feasibility problems with positive-definite constraints
We study a class of projective transformations of spectraplexes associated with self-dual cones and, on this basis, propose a polynomial-time algorithm for convex feasibility problems with positive definite constraints. At each iteration of the algorithm, either a feasible solution is found or a suitable valid inequality inducing a projective transformation allowing to bring the solution set closer to the center of an associated spectraplex. The closeness to the center is measured in terms of a…

Dynamic Optimal Transport with optimal star shaped graphs
Marcello Carioni, Juliane Krautz, Jan-F. Pietschmann
https://arxiv.org/abs/2506.15007 https://

Dynamic Optimal Transport with optimal star shaped graphs
We study an optimal transport problem in a compact convex set $Ω\subset\mathbb{R}^d$ where bulk transport is coupled to dynamic optimal transport on a metric graph $ \mathsf{G} = (\mathsf{V},\mathsf{E})$ which is embedded in $Ω$. We prove existence of solutions for fixed graphs. Next, we consider varying graphs, yet only for the case of star-shaped ones. Here, the action functional is augmented by an additional penalty that prevents the edges of the graph to overlap. This allows to preserve t…

Implicit Constraint-Aware Off-Policy Correction for Offline Reinforcement Learning
Ali Baheri
https://arxiv.org/abs/2506.14058 https://

Implicit Constraint-Aware Off-Policy Correction for Offline Reinforcement Learning
Offline reinforcement learning promises policy improvement from logged interaction data alone, yet state-of-the-art algorithms remain vulnerable to value over-estimation and to violations of domain knowledge such as monotonicity or smoothness. We introduce implicit constraint-aware off-policy correction, a framework that embeds structural priors directly inside every Bellman update. The key idea is to compose the optimal Bellman operator with a proximal projection on a convex constraint set, wh…

No-dimensional Tverberg-type problems
Alexander Polyanskii
https://arxiv.org/abs/2506.13451 https://arxiv.org/pdf/2506.13451

No-dimensional Tverberg-type problems
Recently, Adiprasito et al. have initiated the study of the so-called no-dimensional Tverberg problem. This problem can be informally stated as follows: Given $n\geq k$, partition an $n$-point set in Euclidean space into $k$ parts such that their convex hulls intersect a ball of relatively small radius. In this survey, we aim to present the recent progress towards solving the no-dimensional Tverberg problem and new open questions arising in its context. Also, we discuss the colorful variation…

This https://arxiv.org/abs/2504.03575 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the maximal volume of empty convex bodies amidst multivariate dilates of a lacunary integer sequence
Let \((a_n)_{n \in \mathbb{N}}\) be a lacunary sequence of integers satisfying the Hadamard gap condition. For any fixed dimension $d \geq 1$, we establish asymptotic upper bounds for the maximal gap in the set of dilates \(\{\boldsymbolα a_n \}_{n \leq N}\) modulo 1 as $N \to \infty$, for Lebesgue--almost all dilation vectors $\boldsymbolα \in [0,1]^d$. More precisely, we prove that for any lacunary \((a_n)_{n \in \mathbb{N}}\) and Lebesgue--almost all $\boldsymbolα$, every convex set in $[…

A Diestel-Faires type result for multimeasures
Jos\'e Rodr\'iguez
https://arxiv.org/abs/2506.11872 https://arxiv.org/pdf/2506…

A Diestel-Faires type result for multimeasures
Let $X$ be a real Banach space and let $Y \subseteq X^*$ be a linear subspace having the Orlicz-Thomas property, that is, for each $σ$-algebra $Σ$ and for each map $ν:Σ\to X$, the countable additivity of the composition $x^*\circ ν$ for all $x^*\in Y$ implies the countable additivity of $ν$. We show that the Orlicz-Thomas property allows to test countable additivity of set-valued maps. Namely, if $M$ is a map defined on a $σ$-algebra $Σ$ whose values are convex, $σ(X,Y)$-compact, bound…

Controlled Reach-avoid Set Computation for Discrete-time Polynomial Systems via Convex Optimization
Taoran Wu, Yiling Xue, Dejin Ren, Arvind Easwaran, Martin Fr\"anzle, Bai Xue
https://arxiv.org/abs/2506.06679

Controlled Reach-avoid Set Computation for Discrete-time Polynomial Systems via Convex Optimization
This paper addresses the computation of controlled reach-avoid sets (CRASs) for discrete-time polynomial systems subject to control inputs. A CRAS is a set encompassing initial states from which there exist control inputs driving the system into a target set while avoiding unsafe sets. However, efficiently computing CRASs remains an open problem, especially for discrete-time systems. In this paper, we propose a novel framework for computing CRASs which takes advantage of a probabilistic perspec…

This https://arxiv.org/abs/2306.07237 has been replaced.
link: https://scholar.google.com/scholar?q=a

Three Edge-disjoint Plane Spanning Paths in a Point Set
We consider the following problem: Given a set $S$ of $n$ distinct points in the plane, how many edge-disjoint plane straight-line spanning paths can be drawn on $S$? Each spanning path must be crossing-free, but edges from different paths are allowed to intersect at arbitrary points. It is known that if the points of $S$ are in convex position, then $\lfloor n/2 \rfloor$ such paths always exist. However, for general point sets, the best known construction yields only two edge-disjoint plane sp…

Minimal displacement set for CAT(0) cubical complexes
Ioana-Claudia Lazar
https://arxiv.org/abs/2505.23318 https://arxiv.org/pdf/2505…

Minimal displacement set for CAT(0) cubical complexes
We investigate the structure of the minimal displacement set in CAT(0) cubical complexes. We show that such set is convex, it is locally endowed with a CAT(0) metric and it is simply connected.

On the singular set of the free boundary for a Monge-Amp\`ere obstacle problem
Tianling Jin, Xushan Tu, Jingang Xiong
https://arxiv.org/abs/2506.08387 http…

On the singular set of the free boundary for a Monge-Ampère obstacle problem
This is a continuation of our earlier work [14] on the Monge-Ampère obstacle problem \[ \det D^2 v = v^q χ_{\{v>0\}}, \quad v \geq 0 \text{ convex} \] with $q \in [0,n)$, where we studied the regularity of the strictly convex part of the free boundary. In this work, we examine the non-strictly convex part of the free boundary and establish optimal dimension bounds for its flat portion. Additionally, we investigate the strong maximum principle and a stability property for this Monge-Ampère …

On compact sets possessing $q$-convex functions
Thomas Pawlaschyk, Nikolay Shcherbina
https://arxiv.org/abs/2505.24588 https://arxiv.…

On compact sets possessing $q$-convex functions
We show that there exists a $q$-convex function in a neighborhood of a compact set $K$ in a complex manifold $\mathcal{M}$ if and only if the $q$-nucleus of this compact set is empty. The latter can be characterized as the maximal $q$-pseudoconcave subset of $K$, i.e., a subset of $K$ containing all other compact $q$-pseudoconcave subsets in $K$.

Weak solutions of Stochastic Volterra Equations in convex domains with general kernels
Eduardo Abi Jaber, Aur\'elien Alfonsi, Guillaume Szulda
https://arxiv.org/abs/2506.04911

Weak solutions of Stochastic Volterra Equations in convex domains with general kernels
We establish new weak existence results for $d$-dimensional Stochastic Volterra Equations (SVEs) with continuous coefficients and possibly singular one-dimensional non-convolution kernels. These results are obtained by introducing an approximation scheme and showing its convergence. A particular emphasis is made on the stochastic invariance of the solution in a closed convex set. To do so, we extend the notion of kernels that preserve nonnegativity introduced in \cite{Alfonsi23} to non-convolut…

This https://arxiv.org/abs/2503.16398 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The global convergence time of stochastic gradient descent in non-convex landscapes: Sharp estimates via large deviations
In this paper, we examine the time it takes for stochastic gradient descent (SGD) to reach the global minimum of a general, non-convex loss function. We approach this question through the lens of randomly perturbed dynamical systems and large deviations theory, and we provide a tight characterization of the global convergence time of SGD via matching upper and lower bounds. These bounds are dominated by the most "costly" set of obstacles that the algorithm may need to overcome in order to reach…

Gradient regularity for widely degenerate elliptic partial differential equations
Michael Strunk
https://arxiv.org/abs/2506.11708 https://

Gradient regularity for widely degenerate elliptic partial differential equations
In this paper, we investigate the regularity of weak solutions $u\colonΩ\to\mathbb{R}$ to elliptic equations of the type \begin{equation*} \mathrm{div}\, \nabla \mathcal{F}(x,Du) = f\qquad\text{in $Ω$}, \end{equation*} whose ellipticity degenerates in a fixed bounded and convex set $E\subset\mathbb{R}^n$ with $0\in \mathrm{Int}\, E$. Here, $Ω\subset\mathbb{R}^n$ denotes a bounded domain, and $\mathcal{F} \colon Ω\times\mathbb{R}^n \to\mathbb{R}_{\geq 0}$ is a function with the properties:…

A strengthened bound on the number of states required to characterize maximum parsimony distance
Mareike Fischer, Steven Kelk, Sofia Vazquez Alferez
https://arxiv.org/abs/2506.09888

A strengthened bound on the number of states required to characterize maximum parsimony distance
In this article we prove that the distance $d_{\mathrm{MP}}(T_1,T_2) = k$ between two unrooted binary phylogenetic trees $T_1, T_2$ on the same set of taxa can be defined by a character that is convex on one of $T_1, T_2$ and which has at most $2k$ states. This significantly improves upon the previous bound of $7k-5$ states. We also show that for every $k \geq 1$ there exist two trees $T_1, T_2$ with $d_{\mathrm{MP}}(T_1,T_2) = k$ such that at least $k+1$ states are necessary in any character t…

Trajectory Optimization for UAV-Based Medical Delivery with Temporal Logic Constraints and Convex Feasible Set Collision Avoidance
Kaiyuan Chen, Yuhan Suo, Shaowei Cui, Yuanqing Xia, Wannian Liang, Shuo Wang
https://arxiv.org/abs/2506.06038

Trajectory Optimization for UAV-Based Medical Delivery with Temporal Logic Constraints and Convex Feasible Set Collision Avoidance
This paper addresses the problem of trajectory optimization for unmanned aerial vehicles (UAVs) performing time-sensitive medical deliveries in urban environments. Specifically, we consider a single UAV with 3 degree-of-freedom dynamics tasked with delivering blood packages to multiple hospitals, each with a predefined time window and priority. Mission objectives are encoded using Signal Temporal Logic (STL), enabling the formal specification of spatial-temporal constraints. To ensure safety, c…

This https://arxiv.org/abs/2504.02611 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCG_…

Instance-Optimal Imprecise Convex Hull
Imprecise measurements of a point set P = (p1, ..., pn) can be modelled by a family of regions F = (R1, ..., Rn), where each imprecise region Ri contains a unique point pi. A retrieval models an accurate measurement by replacing an imprecise region Ri with its corresponding point pi. We construct the convex hull of an imprecise point set in the plane, where regions in F may be retrieved at unit cost. The goal is to determine the cyclic ordering of the convex hull vertices of P as efficiently as…

Dual realizations of Bergman spaces on strongly convex domains
Agniva Chatterjee
https://arxiv.org/abs/2506.02913 https://arxiv.org/p…

Dual realizations of Bergman spaces on strongly convex domains
The Fantappiè and Laplace transforms realize isomorphisms between analytic functionals supported on a convex compact set $K\subset{\mathbb C}^n$ and certain spaces of holomorphic functions associated with $K$. Viewing the Bergman space of a bounded domain in ${\mathbb C}^n$ as a subspace of the space of analytic functionals supported on its closure, the images of the restrictions of these transforms have been studied in the planar setting. For the Fantappiè transform, this was done for simply…

This https://arxiv.org/abs/2501.03645 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Big convex polytopes or rich hyperplanes
For natural numbers $n$ and $l > d \geq 2$, let $ES_d(l,n)$ be the minimum $N$ such that any set of at least $N$ points in $\mathbb{R}^d$ contains either $l$ points contained in a common $(d-1)$-dimensional hyperplane or $n$ points in convex position. In this paper, we give the upper and lower bounds for $ES_d(l,n)$.

Discrete and Continuous Difference of Submodular Minimization
George Orfanides, Tim Hoheisel, Marwa El Halabi
https://arxiv.org/abs/2506.07952 https://

Discrete and Continuous Difference of Submodular Minimization
Submodular functions, defined on continuous or discrete domains, arise in numerous applications. We study the minimization of the difference of two submodular (DS) functions, over both domains, extending prior work restricted to set functions. We show that all functions on discrete domains and all smooth functions on continuous domains are DS. For discrete domains, we observe that DS minimization is equivalent to minimizing the difference of two convex (DC) functions, as in the set function cas…

This https://arxiv.org/abs/2503.10126 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

An LiGME Regularizer of Designated Isolated Minimizers -- An Application to Discrete-Valued Signal Estimation
For a regularized least squares estimation of discrete-valued signals, we propose a Linearly involved Generalized Moreau Enhanced (LiGME) regularizer, as a nonconvex regularizer, of designated isolated minimizers. The proposed regularizer is designed as a Generalized Moreau Enhancement (GME) of the so-called sum-of-absolute-values (SOAV) convex regularizer. Every candidate vector in the discrete-valued set is aimed to be assigned to an isolated local minimizer of the proposed regularizer while …

This https://arxiv.org/abs/2502.10382 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On creating convexity in high dimensions
Given a subset $A$ of $\mathbb{R}^n$, we define \begin{align*} \mathrm{conv}_k(A) := \left\{ λ_1 s_1 + \cdots + λ_k s_k : λ_i \in [0,1], \sum_{i=1}^k λ_i = 1 , s_i \in A \right\} \end{align*} to be the set of vectors in $\mathbb{R}^n$ that can be written as a $k$-fold convex combination of vectors in $A$. Let $γ_n$ denote the standard Gaussian measure on $\mathbb{R}^n$. We show that for every $\varepsilon > 0$, there exists a subset $A$ of $\mathbb{R}^n$ with Gaussian measure $γ_n(A) \geq…

This https://arxiv.org/abs/2408.03218 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Limit theorems for the number of crossings and stress in projections of the random geometric graph
We consider the number of edge crossings in a random graph drawing generated by projecting a random geometric graph on some compact convex set $W\subset \mathbb{R}^d$, $d\geq 3$, onto a plane. The positions of these crossings form the support of a point process. We show that if the expected number of crossings converges to a positive but finite value, this point process converges to a Poisson point process in the Kantorovich-Rubinstein distance. We further show a multivariate central limit theo…

This https://arxiv.org/abs/2410.05132 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the uniqueness of tangent cones to area minimizing currents at boundaries with arbitrary multiplicity
We consider an area minimizing current $T$ in a $C^2$ submanifold $Σ$ of $\mathbb{R}^{m+n}$, with arbitrary integer boundary multiplicity $\partial T = Q [\![ Γ]\!]$ where $Γ$ is a $C^2$ submanifold of $Σ$. We show that at every density $Q/2$ boundary point the tangent cone to $T$ is unique and there is a power rate of convergence to the unique tangent cone. In particular, if $Γ$ is a closed manifold which lies at the boundary of a uniformly convex set $Ω$ and $Σ=\mathbb{R}^{m+n}$ then…

This https://arxiv.org/abs/2410.22038 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Cramér-Wold theorem for mixtures
We show how a Cramér-Wold theorem for a family of multivariate probability distributions can be used to generate a similar theorem for mixtures (convex combinations) of distributions drawn from the same family. Using this abstract result, we establish a Cramér-Wold theorem for mixtures of multivariate Gaussian distributions. According to this theorem, two such mixtures can be distinguished by projecting them onto a certain predetermined finite set of lines, the number of lines depending onl…

This https://arxiv.org/abs/2409.06512 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Manifolds of absolutely continuous functions with values in an infinite-dimensional manifold and regularity properties of half-Lie groups
For $p\in [1,\infty]$, we define a smooth manifold structure on the set $AC_{L^p}([a,b],N)$ of absolutely continuous functions $γ\colon [a,b]\to N$ with $L^p$-derivatives for all real numbers $a

This https://arxiv.org/abs/2406.10065 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An Extended Validity Domain for Constraint Learning
We consider embedding a predictive machine-learning model within a prescriptive optimization problem. In this setting, called constraint learning, we study the concept of a validity domain, i.e., a constraint added to the feasible set, which keeps the optimization close to the training data, thus helping to ensure that the computed optimal solution exhibits less prediction error. In particular, we propose a new validity domain which uses a standard convex-hull idea but in an extended space. We …

This https://arxiv.org/abs/2406.10065 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An Extended Validity Domain for Constraint Learning
We consider embedding a predictive machine-learning model within a prescriptive optimization problem. In this setting, called constraint learning, we study the concept of a validity domain, i.e., a constraint added to the feasible set, which keeps the optimization close to the training data, thus helping to ensure that the computed optimal solution exhibits less prediction error. In particular, we propose a new validity domain which uses a standard convex-hull idea but in an extended space. We …