Related papers: Decomposition of Large Scale Linear Programming Pr…

This study investigates imposing hard inequality constraints on the outputs of convolutional neural networks (CNN) during training. Several recent works showed that the theoretical and practical advantages of Lagrangian optimization over…

(Renyi Qu's Master's Thesis) Recent advancements in interpretable models for vision-language tasks have achieved competitive performance; however, their interpretability often suffers due to the reliance on unstructured text outputs from…

Modern neural networks have revolutionized the fields of computer vision (CV) and Natural Language Processing (NLP). They are widely used for solving complex CV tasks and NLP tasks such as image classification, image generation, and machine…

Many approaches to transform classification problems from non-linear to linear by feature transformation have been recently presented in the literature. These notably include sparse coding methods and deep neural networks. However, many of…

The strengthening of linear relaxations and bounds of mixed integer linear programs has been an active research topic for decades. Enumeration-based methods for integer programming like linear programming-based branch-and-bound exploit…

This paper considers the problem of distributed source coding for a large network. A major obstacle that poses an existential threat to practical deployment of conventional approaches to distributed coding is the exponential growth of the…

Neural networks (NNs) have gained significant attention across various engineering disciplines, particularly in design optimization, where they are used to build surrogate models for high-dimensional regression problems. Despite their power…

Uncertainty decomposition refers to the task of decomposing the total uncertainty of a predictive model into aleatoric (data) uncertainty, resulting from inherent randomness in the data-generating process, and epistemic (model) uncertainty,…

We show how to extract alternative solutions for optimization problems solved by Benders Decomposition. In practice, alternative solutions provide useful insights for complex applications; some solvers do support generation of alternative…

We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program. Such problems occur naturally in many scientific and web applications. Although there are efficient methods which tackle this problem, they are…

Diffusion large language models (dLLMs) have recently emerged as a promising alternative to autoregressive (AR) models, offering advantages such as accelerated parallel decoding and bidirectional context modeling. However, the vanilla…

Dantzig-Wolfe decomposition (DWD) is a classical algorithm for solving large-scale linear programs whose constraint matrix involves a set of independent blocks coupled with a set of linking rows. The algorithm decomposes such a model into a…

Linear Programming (LP) decoding of Low-Density Parity-Check (LDPC) codes has attracted much attention in the research community in the past few years. LP decoding has been derived for binary and nonbinary linear codes. However, the most…

We propose a general dual ascent framework for Lagrangean decomposition of combinatorial problems. Although methods of this type have shown their efficiency for a number of problems, so far there was no general algorithm applicable to…

Linear programming (LP) decoding approximates maximum-likelihood (ML) decoding of a linear block code by relaxing the equivalent ML integer programming (IP) problem into a more easily solved LP problem. The LP problem is defined by a set of…

This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…

Tensor decompositions are promising tools for big data analytics as they bring multiple modes and aspects of data to a unified framework, which allows us to discover complex internal structures and correlations of data. Unfortunately most…

In optimization problems, some variable subsets may have a joint non-linear or non-monotonical influence on the function value. Therefore, knowledge of variable dependencies may be crucial for effective optimization, and many…

Multiple patterning lithography has been widely adopted in advanced technology nodes of VLSI manufacturing. As a key step in the design flow, multiple patterning layout decomposition (MPLD) is critical to design closure. Due to the…

Discrete Combinatorial Problems (DCPs) are prevalent in industrial decision-making and optimisation. However, while constraint solving technologies for DCPs have advanced significantly, the core process of formalising them, namely…