A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Develops a first-order interior-point method for solving constrained variational inequalities.
New method solves optimization problems with stochastic objectives and constraints.
This paper reverses a construction by merging boundary critical points into an interior one.
In this paper, we study reinforcement learning (RL) algorithms to solve real-world decision problems with the objective of maximizing the long-term reward as well as satisfying cumulative constraints. We propose a novel first-order policy optimization method, Interior-point Policy Optimization (IPO), which augments the…
We construct non-trapping asymptotically hyperbolic manifolds with boundary conjugate points but no interior conjugate points.
Computing the Wasserstein barycenter of a set of probability measures under the optimal transport metric can quickly become prohibitive for traditional second-order algorithms, such as interior-point methods, as the support size of the measures increases. In this paper, we overcome the difficulty by developing a new ad…
Interior-point methods adapted for manifolds, achieving similar optimization results.
IPMs struggle with hyperbolic spaces due to polynomially growing barrier parameters.
The study confirms conjectures about normals to convex polytopes in 3D space.
Book covers tools for zeroth-order convex optimisation.
In this article we compute the best Sobolev constants for various Hardy-Sobolev inequalities with sharp Hardy term. This is carried out in three different environments: interior point singularity in Euclidean space, interior point singularity in hyperbolic space and boundary point singularity in Euclidean domains.
The paper trains neural networks with robustness guarantees using semidefinite constraints.
Many problems in statistical learning, imaging, and computer vision involve the optimization of a non-convex objective function with singularities at the boundary of the feasible set. For such challenging instances, we develop a new interior-point technique building on the Hessian-barrier algorithm recently introduced …
We consider classification tasks in the regime of scarce labeled training data in high dimensional feature space, where specific expert knowledge is also available. We propose a new hybrid optimization algorithm that solves the elastic-net support vector machine (SVM) through an alternating direction method of multipli…
Study on abnormal curves in sub-Riemannian manifolds, proving length-minimizing properties.
We study Hessian fully nonlinear uniformly elliptic equations and show that the second derivatives of viscosity solutions of those equations (in 12 or more dimensions) can blow up in an interior point of the domain. We prove that the optimal interior regularity of such solutions is no more than C^{1+ε}, showing the opt…
Study proves rigidity of critical points in hydrophobic capillary systems.
Graph neural networks improve solving linear optimization problems.
The paper finds curves minimizing elastic energy pinned at endpoints.
The paper examines how to protect LASSO-based feature selection from adversarial attacks.
In this paper we construct examples of deformations of Lorentzian hypersurfaces which are embeddable at all points outside an arbitrarily small compact set whose interior contains a point where embeddablity is not possible.
Study optimal semi-static hedging for illiquid markets using dynamic cash and static quoted derivatives.
A novel one-class classifier fusion method for robust anomaly detection.
Bound critical points for minimal Radó functions.
The first result is the semicontinuity of automorphism groups for the collection of complex two-dimensional bounded pseudoconvex domains with smooth boundary of finite D'Angelo type. The method of proof is new so that it simplifies the previous proof of earlier semicontinuity theorems on bounded strongly pseudoconvex d…
Study geodesics in sub-Riemannian manifolds, resolving open questions.
We use elementary methods to construct a minimal lamination of the interior of a positive cone in R3.
In Minkowski geometry the unit ball is a compact convex body containing the origin in its interior. The boundary of the body is formed by the unit vectors. We also have a so-called Minkowski functional to measure the length of vectors. By changing the origin in the interior of the body we have a smoothly varying fa…
For a Jordan domain in the plane the length metric space of points connected to an interior point by a curve of finite length is a CAT(0)space and Gromov hyperbolic. With respect to the cone topology, that space plus its boundary at infinity is topologically the same as the original Jordan domain.
2-regular points found in spaces with lower Ricci curvature bound.
Study infinitesimal characters on semi-groups to prove interior properties and apply to Teichmüller spaces.
We establish interior Lipschitz regularity for continuous viscosity solutions of fully nonlinear, conformally invariant, degenerate elliptic equations. As a by-product of our method, we also prove a weak form of the strong comparison principle, which we refer to as the principle of propagation of touching points, for o…
The Brouwer fixed point theorem says that any continuous function from disc to itself has a fixed point. By using simple geometrical technique we have generalized the result in manifold and proved that any continuous function on the boundary of a bounded convex domain of a -dimensional Riemannian manifold with a pol…
We provide a direct proof of a non-collapsing estimate for compact hypersurfaces with positive mean curvature moving under the mean curvature flow: Precisely, if every point on the initial hypersurface admits an interior sphere with radius inversely proportional to the mean curvature at that point, then this remains tr…
Given a convex set and an interior point close to the boundary, we prove the existence of a supporting hyperplane whose distance to the point is controlled, in a dimensionally quantified way, by the thickness of the convex set in the orthogonal direction. This result has important applications in the regularity theory …
Novel methods generate diverse policies in reinforcement learning.
We develop a structure theory for RCD spaces with curvature bounded above in Alexandrov sense. In particular, we show that any such space is a topological manifold with boundary whose interior is equal to the set of regular points. Further the set of regular points is a smooth manifold and is geodesically convex. Aroun…
We prove a geometric model for HHS hierarchies as CAT(0) cube complexes.
In this paper we consider the problem of minimizing the relative perimeter under a volume constraint in the interior of a convex body, i.e., a compact convex set in Euclidean space with interior points. We shall not impose any regularity assumption on the boundary of the convex set. Amongst other results, we shall prov…
New formula simplifies interior polynomial calculation.
Paper proves unique energy-minimizing curves in constrained spaces.
New estimate for Curve Shortening Flow improves graphical solutions.
Study min-max theory for hypersurfaces with boundary constraints.
We study the Birman exact sequence for compact --manifolds, obtaining a complete picture of the relationship between the mapping class group of the manifold and the mapping class group of the submanifold obtained by deleting an interior point. This covers both orientable manifolds and non-orientable ones.
Hot spots conjecture proven for small eigenvalue domains.
Estimates for special Lagrangian curvature equations in critical and convex cases.
Develops consistent approximations for composite optimization problems.
We consider embedded hypersurfaces evolving by fully nonlinear flows in which the normal speed of motion is a homogeneous degree one, concave or convex function of the principal curvatures, and prove a non-collapsing estimate: Precisely, the function which gives the curvature of the largest interior sphere touching the…