Related papers: Breaking the 2-loop barrier for generalized IBP re…
In this paper, we design, analyze, and implement a variant of the two-loop L-shaped algorithms for solving two-stage stochastic programming problems that arise from important application areas including revenue management and power systems.…
A polynomial-time algorithm is produced which, given generators for a group of permutations on a finite set, returns a direct product decomposition of the group into directly indecomposable subgroups. The process uses bilinear maps and…
For loop integrals, the standard method is reduction. A well-known reduction method for one-loop integrals is the Passarino-Veltman reduction. Inspired by the recent paper [1] where the tadpole reduction coefficients have been solved, in…
Bilevel optimization has gained significant attention in recent years due to its broad applications in machine learning. This paper focuses on bilevel optimization in decentralized networks and proposes a novel single-loop algorithm for…
Splitting methods have emerged as powerful tools to address complex problems by decomposing them into smaller solvable components. In this work, we develop a general approach to forward-backward splitting methods for solving monotone…
We describe a general analytic-numerical reduction scheme for evaluating any 2-loop diagrams with general kinematics and general renormalizable interactions, whereby ten special functions form a complete set after tensor reduction. We…
In this paper, we suggest a new efficient algorithm in order to compute S-polynomial reduction rapidly in the known algorithm for computing Grobner bases, and compare the complexity with others.
This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…
We show that for a class of two-loop diagrams, the on-shell part of the integration-by-parts (IBP) relations correspond to exact meromorphic one-forms on algebraic curves. Since it is easy to find such exact meromorphic one-forms from…
Hyperparameter tuning is an important task of machine learning, which can be formulated as a bilevel program (BLP). However, most existing algorithms are not applicable for BLP with non-smooth lower-level problems. To address this, we…
This article presents a validation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem. The proposed algorithm is an implicit reduction procedure that combines primal and dual linear…
We present LinApart2, a major update to the LinApart algorithm for univariate partial fraction decomposition. Unlike its predecessor, LinApart2 can handle denominators of arbitrary polynomial degree without explicit factorization, while…
We present an approach to construct efficient sparse summation-by-parts (SBP) operators on triangles and tetrahedra with a tensor-product structure. The operators are constructed by splitting the simplices into quadrilateral or hexahedral…
We introduce and systematically develop two classes of discrete integrable operators: those with $2\times 2$ matrix kernels and those possessing general differential kernels, thereby generalizing the discrete analogue previously studied. A…
Summation-by-parts (SBP) operators allow us to systematically develop energy-stable and high-order accurate numerical methods for time-dependent differential equations. Until recently, the main idea behind existing SBP operators was that…
As a key method to deal with loop integrals, Integration-By-Parts (IBP) method can be used to do reduction as well as establish the differential equations for master integrals. However, when talking about tensor reduction, the…
Standard integration-by-parts (IBP) reduction methods typically yield Feynman integral bases where the reduction of some integrals gives rise to coefficients singular as the dimensional regulator $\epsilon\rightarrow 0$. These singular…
The artificial neural network is a popular framework in machine learning. To empower individual neurons, we recently suggested that the current type of neurons could be upgraded to 2nd order counterparts, in which the linear operation…
We have been working in many aspects of the problem of analyzing, understanding and solving ordinary differential equations (first and second order). As we have extensively mentioned, while working in the Darboux type methods, the most…
In contrast with many other convex optimization classes, state-of-the-art semidefinite programming solvers are yet unable to efficiently solve large scale instances. This work aims to reduce this scalability gap by proposing a novel…