Related papers: A Variational-Calculus Approach to Online Algorith…

In this paper, we study the problem of minimizing a sum of convex objective functions, which are locally available to agents in a network. Distributed optimization algorithms make it possible for the agents to cooperatively solve the…

To construct a parallel approach for solving optimization problems with orthogonality constraints is usually regarded as an extremely difficult mission, due to the low scalability of the orthonormalization procedure. However, such demand is…

A new scaling and recovering algorithm is proposed for simultaneously computing the matrix $\varphi$-functions that arise in exponential integrator methods for the numerical solution of certain first-order systems of ordinary differential…

Low-rank matrix approximation is a fundamental tool in data analysis for processing large datasets, reducing noise, and finding important signals. In this work, we present a novel truncated LU factorization called Spectrum-Revealing LU…

Learning to Rank (LTR) methods generally assume that each document in a top-K ranking is presented in an equal format. However, previous work has shown that users' perceptions of relevance can be changed by varying presentations, i.e.,…

The article provides a solution algorithm for the linear programming problem (LPP) with the latter being presented as an antagonistic matrix game so the game's further solution is based on the iterative method. The algorithm is presented as…

Despite the success, the process of fine-tuning large-scale PLMs brings prohibitive adaptation costs. In fact, fine-tuning all the parameters of a colossal model and retaining separate instances for different tasks are practically…

We present an online preconditioning technique for the primal-dual hybrid gradient (PDHG) algorithm for linear programming (LP). The method adaptively updates primal and dual preconditioners using an online optimization framework. To…

Integer linear programming (ILP) is an elegant approach to solve linear optimization problems, naturally described using integer decision variables. Within the context of physics-inspired machine learning applied to chemistry, we…

We consider differentially private approximate singular vector computation. Known worst-case lower bounds show that the error of any differentially private algorithm must scale polynomially with the dimension of the singular vector. We are…

Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…

Large Language Models (LLMs) show promise for automated code optimization but struggle without performance context. This work introduces Opal, a modular framework that connects performance analytics insights with the vast body of published…

There is a clear need for efficient algorithms to tune hyperparameters for statistical learning schemes, since the commonly applied search methods (such as grid search with N-fold cross-validation) are inefficient and/or approximate.…

We consider the primal and dual forms of the optimality conditions for PDE-contrained optimization problems arising in Data-Driven Computational Mechanics when specialized to the reaction-diffusion context. Starting with the continuous…

Let A be a matrix, c be any linear objective function and x be a fractional vector, say an LP solution to some discrete optimization problem. Then a recurring task in theoretical computer science (and in approximation algorithms in…

Optimization problems are pervasive in sectors from manufacturing and distribution to healthcare. However, most such problems are still solved heuristically by hand rather than optimally by state-of-the-art solvers because the expertise…

Linear programming has played a key role in the study of algorithms for combinatorial optimization problems. In the field of approximation algorithms, this is well illustrated by the uncapacitated facility location problem. A variety of…

A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum…

This paper provides the first meaningful documentation and analysis of an established technique which aims to obtain an approximate solution to linear programming problems prior to applying the primal simplex method. The underlying…

With the increasing adoption of Large Language Models (LLMs), more customization is needed to ensure privacy-preserving and safe generation. We address this objective from two critical aspects: unlearning of sensitive information and…