相关论文: Parallelized Solution to Semidefinite Programmings…

High-dimensional portfolio optimization faces significant computational challenges under complex constraints, with traditional optimization methods struggling to balance convergence speed and global exploration capability. To address this,…

Recently, in a paper by Jentzen and Kloeden [Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 465 (2009) 649-667], a new method for simulating nearly linear stochastic partial differential equations (SPDEs) with additive noise has been…

An instance-weighted variant of the support vector machine (SVM) has attracted considerable attention recently since they are useful in various machine learning tasks such as non-stationary data analysis, heteroscedastic data modeling,…

We present a new solver for coupled nonlinear elliptic partial differential equations (PDEs). The solver is based on pseudo-spectral collocation with domain decomposition and can handle one- to three-dimensional problems. It has three…

We present a nearly linear work parallel algorithm for approximating the Held-Karp bound for the Metric TSP problem. Given an edge-weighted undirected graph $G=(V,E)$ on $m$ edges and $\epsilon>0$, it returns a $(1+\epsilon)$-approximation…

Despite much research, hard weighted problems still resist super-polynomial improvements over their textbook solution. On the other hand, the unweighted versions of these problems have recently witnessed the sought-after speedups.…

Numerical simulation is dominant in solving partial difference equations (PDEs), but balancing fine-grained grids with low computational costs is challenging. Recently, solving PDEs with neural networks (NNs) has gained interest, yet…

For a symmetric positive semidefinite linear system of equations $\mathcal{Q} {\bf x} = {\bf b}$, where ${\bf x} = (x_1,\ldots,x_s)$ is partitioned into $s$ blocks, with $s \geq 2$, we show that each cycle of the classical block symmetric…

The success of deep learning (DL) is often achieved with large models and high complexity during both training and post-training inferences, hindering training in resource-limited settings. To alleviate these issues, this paper introduces a…

The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…

Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operations research, and optimization. Despite the consistent efforts on this problem, all…

In observational studies, weighting methods that directly optimize the balance between treatment and covariates have received much attention lately; however these have mainly focused on binary treatments. Inspired by domain adaptation, we…

Quantum algorithms to integrate nonlinear PDEs governing flow problems are challenging to discover but critical to enhancing the practical usefulness of quantum computing. We present here a near-optimal, robust, and end-to-end quantum…

In the past years, the application of neural networks as an alternative to classical numerical methods to solve Partial Differential Equations has emerged as a potential paradigm shift in this century-old mathematical field. However, in…

A new approach to solving a class of rankconstrained semi-definite programming (SDP) problems, which appear in many signal processing applications such as transmit beamspace design in multiple-input multiple-output (MIMO) radar, downlink…

Efficient encoding of classical data into quantum circuits is a critical challenge that directly impacts the scalability of quantum algorithms. In this work, we present an automated compilation framework for resource-aware quantum data…

This paper presents a methodology for using varying sample sizes in sequential quadratic programming (SQP) methods for solving equality constrained stochastic optimization problems. The first part of the paper deals with the delicate issue…

We study semidefinite programming (SDP) relaxations for the NP-hard problem of globally optimizing a quadratic function over the Stiefel manifold. We introduce a strengthened relaxation based on two recent ideas in the literature: (i) a…

A numerical framework is developed to solve various types of PDEs on complicated domains, including steady and time-dependent, non-linear and non-local PDEs, with different boundary conditions that can also include non-linear and non-local…

We consider linear-programming (LP) decoding of low-density parity-check (LDPC) codes. While it is clear that one can use any general-purpose LP solver to solve the LP that appears in the decoding problem, we argue in this paper that the LP…