Related papers: Climbing LP Algorithms
This paper considers multiprocessor task scheduling in a multistage hybrid flow-shop environment. The problem even in its simplest form is NP-hard in the strong sense. The great deal of interest for this problem, besides its theoretical…
Neural networks have now long been used for solving complex problems of image domain, yet designing the same needs manual expertise. Furthermore, techniques for automatically generating a suitable deep learning architecture for a given…
The last year has witnessed the rapid progress of large language models (LLMs) across diverse domains. Among them, CodeLLMs have garnered particular attention because they can not only assist in completing various programming tasks but also…
Linear Programming (LP) relaxations have become powerful tools for finding the most probable (MAP) configuration in graphical models. These relaxations can be solved efficiently using message-passing algorithms such as belief propagation…
We develop several efficient algorithms for the classical \emph{Matrix Scaling} problem, which is used in many diverse areas, from preconditioning linear systems to approximation of the permanent. On an input $n\times n$ matrix $A$, this…
There are two primary approaches to solving Markov decision problems (MDPs): dynamic programming based on the Bellman equation and linear programming (LP). Dynamic programming methods are the most widely used and form the foundation of both…
Following the great success of Machine Learning (ML), especially Deep Neural Networks (DNNs), in many research domains in 2010s, several ML-based approaches were proposed for detection in large inverse linear problems, e.g., massive MIMO…
Linear programming (LP) relaxation is a standard technique for solving hard combinatorial optimization (CO) problems. Here we present a gradient descent algorithm which exploits the special structure of some LP relaxations induced by CO…
The paper proposes a new algorithm for solving global univariate optimization problems. The algorithm does not require convexity of the target function. For a broad variety of target functions after performing (if necessary) several…
Rounding linear programs using techniques from discrepancy is a recent approach that has been very successful in certain settings. However this method also has some limitations when compared to approaches such as randomized and iterative…
Large Language Models have shown remarkable capabilities in the NLP domain. Their effectiveness can mainly be attributed to their ability to adapt to an array of downstream tasks. However, generally, full fine-tuning is a computationally…
We consider the problem of designing an adaptive sequence of questions that optimally classify a candidate's ability into one of several categories or discriminative grades. A candidate's ability is modeled as an unknown parameter, which,…
Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…
The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
Packing and covering linear programs (PC-LPs) form an important class of linear programs (LPs) across computer science, operations research, and optimization. In 1993, Luby and Nisan constructed an iterative algorithm for approximately…
We consider large linear and nonlinear fixed point problems, and solution with proximal algorithms. We show that there is a close connection between two seemingly different types of methods from distinct fields: 1) Proximal iterations for…
Dynamic programming (DP) is a fundamental method in operations research, but formulating DP models has traditionally required expert knowledge of both the problem context and DP techniques. Large Language Models (LLMs) offer the potential…
Large Language Models (LLMs) have shown impressive performance as general purpose agents, but their abilities remain highly dependent on prompts which are hand written with onerous trial-and-error effort. We propose a simple and…
The Chambolle-Pock algorithm (CPA), also known as the primal-dual hybrid gradient method, has gained popularity over the last decade due to its success in solving large-scale convex structured problems. This work extends its convergence…
We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modeled by differential equations. The algorithm relies…