相关论文: $\texttt{TRIQS}/\texttt{SOM}$: Implementation of t…

Structural equation modeling (SEM) is a popular tool in the social and behavioural sciences, where it is being applied to ever more complex data types. The high-dimensional data produced by modern sensors, brain images, or (epi)genetic…

Determining whether a given program terminates is the quintessential undecidable problem. Algorithms for termination analysis are divided into two groups: (1) algorithms with strong behavioral guarantees that work in limited circumstances…

Thomson problem is a classical problem in physics to study how $n$ number of charged particles distribute themselves on the surface of a sphere of $k$ dimensions. When $k=2$, i.e. a 2-sphere (a circle), the particles appear at equally…

Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…

We present a Gaussian-basis implementation of orbital-free density-functional theory (OF-DFT) in which the trust-region image method (TRIM) is used for optimization. This second-order optimization scheme has been constructed to provide…

We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…

Semi-discrete optimal transport (SOT), which maps a continuous probability measure to a discrete one, is a fundamental problem with wide-ranging applications. Entropic regularization is often employed to solve the SOT problem, leading to a…

We introduce iterative methods named TriCG and TriMR for solving symmetric quasi-definite systems based on the orthogonal tridiagonalization process proposed by Saunders, Simon and Yip in 1988. TriCG and TriMR are tantamount to…

This paper delves into the realm of stochastic optimization for compositional minimax optimization - a pivotal challenge across various machine learning domains, including deep AUC and reinforcement learning policy evaluation. Despite its…

Large Language Models (LLMs) have driven substantial progress in artificial intelligence in recent years, exhibiting impressive capabilities across a wide range of tasks, including mathematical problem-solving. Inspired by the success of…

Anderson mixing (AM) is an acceleration method for fixed-point iterations. Despite its success and wide usage in scientific computing, the convergence theory of AM remains unclear, and its applications to machine learning problems are not…

Combinatorial optimization problems are prevalent across a wide variety of domains. These problems are often nuanced, their optimal solutions might not be efficiently obtainable, and they may require lots of time and compute resources to…

Test suites tend to grow when software evolves, making it often infeasible to execute all test cases with the allocated testing budgets, especially for large software systems. Test suite minimization (TSM) is employed to improve the…

An optimization algorithm for a group of nonsmooth nonconvex problems inspired by two-stage stochastic programming problems is proposed. The main challenges for these problems include (1) the problems lack the popular lower-type properties…

This paper presents algorithms that upper-bound the peak value of a state function along trajectories of a continuous-time system with rational dynamics. The finite-dimensional but nonconvex peak estimation problem is cast as a convex…

Particle-optimization-based sampling (POS) is a recently developed effective sampling technique that interactively updates a set of particles. A representative algorithm is the Stein variational gradient descent (SVGD). We prove, under…

Simple and robust algorithms are developed for compressible Euler equations with the stiffened gas equation of state (EOS), representing gaseous mixtures in thermal equilibrium and without chemical reactions. These algorithms use a fully…

We propose Slim Graph: the first programming model and framework for practical lossy graph compression that facilitates high-performance approximate graph processing, storage, and analytics. Slim Graph enables the developer to express…

In this paper we provide new quantum algorithms with polynomial speed-up for a range of problems for which no such results were known, or we improve previous algorithms. First, we consider the approximation of the frequency moments $F_k$ of…

Stochastic optimization is an important task in many optimization problems where the tasks are not expressible as convex optimization problems. In the case of non-convex optimization problems, various different stochastic algorithms like…