Related papers: An effective method for computing Grothendieck poi…

We propose a novel optimization algorithm for continuous functions using geodesics and contours under conformal mapping.The algorithm can find multiple optima by first following a geodesic curve to a local optimum then traveling to the next…

We describe an algorithm for computing parameter-test-ideals in certain local Cohen-Macaulay rings. The algorithm is based on the study of a Frobenius map on the injective hull of the residue field of the ring and on the application of…

Numerical continuation in the context of optimization can be used to mitigate convergence issues due to a poor initial guess. In this work, we extend this idea to Riemannian optimization problems, that is, the minimization of a target…

Geometric duality theory for multiple objective linear programming problems turned out to be very useful for the development of efficient algorithms to generate or approximate the whole set of nondominated points in the outcome space. This…

An approach to the classification problem of machine learning, based on building local classification rules, is developed. The local rules are considered as projections of the global classification rules to the event we want to classify. A…

Shape optimization is commonly applied in engineering to optimize shapes with respect to an objective functional relying on PDE solutions. In this paper, we view shape optimization as optimization on Riemannian shape manifolds. We consider…

This paper explores variants of the subspace iteration algorithm for computing approximate invariant subspaces. The standard subspace iteration approach is revisited and new variants that exploit gradient-type techniques combined with a…

This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…

Persistent (co)homology is a central construction in topological data analysis, where it is used to quantify prominence of features in data to produce stable descriptors suitable for downstream analysis. Persistence is challenging to…

We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which…

We prove a local duality for some schemes associated to a 2-dimensional complete local ring whose residue field is an n-dimensional local field in the sense of Kato-Parshin. Our results generalize the Saito works in the case n=0 and are…

We present the first local problem that shows a super-constant separation between the classical randomized LOCAL model of distributed computing and its quantum counterpart. By prior work, such a separation was known only for an artificial…

This paper initiates a systematic development of a theory of non-commutative optimization. It aims to unify and generalize a growing body of work from the past few years which developed and analyzed algorithms for natural geodesically…

Let Q be an affine semigroup generating Z^d, and fix a finitely generated Z^d-graded module M over the semigroup algebra k[Q] for a field k. We provide an algorithm to compute a minimal Z^d-graded injective resolution of M up to any desired…

This paper mainly addresses the distributed online optimization problem where the local objective functions are assumed to be convex or non-convex. First, the distributed algorithms are proposed for the convex and non-convex situations,…

Let $R=k[x_1,\dots,x_n]$ be a ring of polynomials over a field $k$ of characteristic $p>0$. There is an algorithm due to Lyubeznik for deciding the vanishing of local cohomology modules $H^i_I(R)$ where $I\subset R$ is an ideal. This…

In this paper, we construct a local ring $A$ such that the kernel of the map $G_0(A)\subq \to G_0(\hat{A})\subq$ is not zero, where $\hat{A}$ is the comletion of $A$ with respect to the maximal ideal, and $G_0()\subq$ is the Grothendieck…

This paper addresses a multi-scale finite element method for second order linear elliptic equations with arbitrarily rough coefficient. We propose a local oversampling method to construct basis functions that have optimal local…

An important problem in computational topology is to calculate the homology of a space from samples. In this work, we develop a statistical approach to this problem by calculating the expected rank of an induced map on homology from a…

In this article we introduce a new type of cyclic contraction mapping on a pair of subsets of a metric space with a graph and prove best proximity points results for the same. Also, we demonstrate that the number of such points is same with…