Related papers: NEP: a module for the parallel solution of nonline…

In this paper, a novel multigrid method based on Newton iteration is proposed to solve nonlinear eigenvalue problems. Instead of handling the eigenvalue $\lambda$ and eigenfunction $u$ separately, we treat the eigenpair $(\lambda, u)$ as…

Answer Set Programming (ASP) is a powerful paradigm for non-monotonic reasoning. Recently, large language models (LLMs) have demonstrated promising capabilities in logical reasoning. Despite this potential, current evaluations of LLM…

The nonlinear eigenvalue problem of a class of second order semi-transcendental differential equations is studied. A nonlinear eigenvalue is defined as the initial condition which gives rise a separatrix solution. A semi-transcendental…

The open-source nonlinear solver Ipopt (https://projects.coin-or.org/Ipopt) is a widely-used software package for the solution of large-scale non-linear optimization problems. At its heart, it employs a third-party linear solver to solve a…

We present a novel approach to accelerate iterative methods to solve nonlinear Schr\"odinger eigenvalue problems using neural networks. Nonlinear eigenvector problems are fundamental in quantum mechanics and other fields, yet conventional…

We consider algorithmic problems motivated by modular robotic reconfiguration in the sliding square model, in which we are given $n$ square-shaped modules in a (labeled or unlabeled) start configuration and need to find a schedule of…

We develop a novel formulation of the Performance Estimation Problem (PEP) for decentralized optimization whose size is independent of the number of agents in the network. The PEP approach allows computing automatically the worst-case…

We formulate and study non-linear paging - a broad model of online paging where the size of subsets of pages is determined by a monotone non-linear set function of the pages. This model captures the well-studied classic weighted paging and…

Mixed integer nonlinear programming (MINLP) problems are encountered in modeling a physical/industrial process consisting both nonlinearity and discrete selective parameters. There are variety of algorithms for solving MINLP problems most…

Spectral Embedding (SE) is a popular method for dimensionality reduction, applicable across diverse domains. Nevertheless, its current implementations face three prominent drawbacks which curtail its broader applicability: generalizability…

Designing and implementing efficient, provably correct parallel neural network processing is challenging. Existing high-level parallel abstractions like MapReduce are insufficiently expressive while low-level tools like MPI and Pthreads…

A growing number of problems in computational mathematics can be reduced to the solution of many linear systems that are related, often depending smoothly or slowly on a parameter $p$, that is, $A(p)x(p)=b(p)$. We introduce an efficient…

In this chapter we are examining several iterative methods for solving nonlinear eigenvalue problems. These arise in variational image-processing, graph partition and classification, nonlinear physics and more. The canonical eigenproblem we…

In this paper, we address the challenge of solving large-scale graph-structured nonlinear programs (gsNLPs) in a scalable manner. GsNLPs are problems in which the objective and constraint functions are associated with nodes on a graph and…

We analyze the performance of two strategies in solving the structured eigenvalue problem deriving from the Bethe-Salpeter equation (BSE) in condensed matter physics. The BSE matrix is constructed with the Yambo code, and the two strategies…

Many Natural Language Processing (NLP) tasks depend on using Named Entities (NEs) that are contained in texts and in external knowledge sources. While this is easy for humans, the present neural methods that rely on learned word embeddings…

The work we describe here is a part of a research program of developing foundations of declarative solving of search problems. We consider the model expansion task as the task representing the essence of search problems where we are given…

As multicore computing is now standard, it seems irresponsible for constraints researchers to ignore the implications of it. Researchers need to address a number of issues to exploit parallelism, such as: investigating which constraint…

The computational inefficiency of spiking neural networks (SNNs) is primarily due to the sequential updates of membrane potential, which becomes more pronounced during extended encoding periods compared to artificial neural networks (ANNs).…

In this paper, we present a novel parallel augmented subspace method and build a package Parallel Augmented Subspace Eigensolver (PASE) for solving large scale eigenvalue problems by the massively parallel finite element discretization.…