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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…
A method of embedding partially ordered sets into linear spaces is presented. The problem of finding all orthocomplementations in a finite lattice is reduced to a linear programming problem.
This article discusses ability of Linear Programming models to be used as solvers of NP-complete problems. Integer Linear Programming is known as NP-complete problem, but non-integer Linear Programming problems can be solved in polynomial…
Factor-revealing linear programs (LPs) and policy-revealing LPs arise in various contexts of algorithm design and analysis. They are commonly used techniques for analyzing the performance of approximation and online algorithms, especially…
Many problems of interest for cyber-physical network systems can be formulated as Mixed Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithm to solve this class…
This paper surveys the trend of leveraging machine learning to solve mixed integer programming (MIP) problems. Theoretically, MIP is an NP-hard problem, and most of the combinatorial optimization (CO) problems can be formulated as the MIP.…
Large Language Models (LLMs) have shown remarkable capabilities in solving various programming tasks, such as code generation. However, their potential for code optimization, particularly in performance enhancement, remains largely…
We study the problem of coded caching when the server has access to several libraries and each user makes independent requests from every library. The single-library scenario has been well studied and it has been proved that coded caching…
We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main algorithms do not require any additional information or…
It has been verified that the linear programming (LP) is able to formulate many real-life optimization problems, which can obtain the optimum by resorting to corresponding solvers such as OptVerse, Gurobi and CPLEX. In the past decades, a…
Many nonlinear optimal control and optimization problems involve constraints that combine continuous dynamics with discrete logic conditions. Standard approaches typically rely on mixed-integer programming, which introduces scalability…
A principled method to obtain approximate solutions of general constrained integer optimization problems is introduced. The approach is based on the calculation of a mean field probability distribution for the decision variables which is…
The problem of space-optimal jump encoding in the x86 instruction set, also known as branch displacement optimization, is described, and a linear-time algorithm is given that uses no complicated data structures, no recursion, and no…
The Lean mathematical library Mathlib is one of the fastest-growing libraries of formalised mathematics. We describe various strategies to manage this growth, while allowing for change and avoiding maintainer overload. This includes dealing…
We generalize the reduction mechanism for linear programming problems and semidefinite programming problems from [arXiv:1410.8816] in two ways 1) relaxing the requirement of affineness and 2) extending to fractional optimization problems.…
While several classes of integer linear optimization problems are known to be solvable in polynomial time, far fewer tractability results exist for integer nonlinear optimization. In this work, we narrow this gap by identifying a broad…
Machine learning components commonly appear in larger decision-making pipelines; however, the model training process typically focuses only on a loss that measures accuracy between predicted values and ground truth values. Decision-focused…
Computational models of human language often involve combinatorial problems. For instance, a probabilistic parser may marginalize over exponentially many trees to make predictions. Algorithms for such problems often employ dynamic…
We study a structured linear program (LP) that emerges in the need of ranking candidates or items in personalized recommender systems. Since the candidate set is only known in real time, the LP also needs to be formed and solved in real…
Integer Linear Programming (ILP) has a broad range of applications in various areas of artificial intelligence. Yet in spite of recent advances, we still lack a thorough understanding of which structural restrictions make ILP tractable.…