Related papers: Progress in Mathematical Programming Solvers from …
Inverse optimization is the problem of determining the values of missing input parameters for an associated forward problem that are closest to given estimates and that will make a given target vector optimal. This study is concerned with…
This article studies a combination of the two state-of-the-art algorithms for the exact solution of linear programs (LPs) over the rational numbers, i.e., without any roundoff errors or numerical tolerances. By integrating the method of…
Approximate linear programming (ALP) is an efficient approach to solving large factored Markov decision processes (MDPs). The main idea of the method is to approximate the optimal value function by a set of basis functions and optimize…
Mixed Integer Linear Programming (MILP) is essential for modeling complex decision-making problems but faces challenges in computational tractability and requires expert formulation. Current deep learning approaches for MILP focus on…
Machine learning (ML) now pervades the field of Automated Program Repair (APR). Algorithms deploy neural machine translation and large language models (LLMs) to generate software patches, among other tasks. But, there are important…
A trend in high performance computers that is becoming increasingly popular is the use of symmetric multiprocessing (SMP) rather than the older paradigm of MPP. MPI codes that ran and scaled well on MPP machines can often be run on an SMP…
Mixed integer convex and nonlinear programs, MICP and MINLP, are expressive but require long solving times. Recent work that combines learning methods on solver heuristics has shown potential to overcome this issue allowing for applications…
Artificial Intelligence (AI) has recently become a real formal science: the new millennium brought the first mathematically sound, asymptotically optimal, universal problem solvers, providing a new, rigorous foundation for the previously…
We have developed a gravity solver based on combining the well developed Particle-Mesh (PM) method and TREE methods. It is designed for and has been implemented on parallel computer architectures. The new code can deal with tens of millions…
Machine learning (ML) is successful in achieving human-level performance in various fields. However, it lacks the ability to explain an outcome due to its black-box nature. While existing explainable ML is promising, almost all of these…
Despite progress in language model (LM) capabilities, evaluations have thus far focused on models' performance on tasks that humans have previously solved, including in programming (Jimenez et al., 2024) and mathematics (Glazer et al.,…
Quadratic Programs (QPs) have become a mature technology for the control of robots of all kinds, including humanoid robots. One aspect has been largely overlooked, however, which is the accuracy with which these QPs should be solved. QP…
Training machine learning (ML) algorithms is a computationally intensive process, which is frequently memory-bound due to repeatedly accessing large training datasets. As a result, processor-centric systems (e.g., CPU, GPU) suffer from…
Most state-of-the-art branch-and-bound solvers for mixed-integer linear programming rely on limited-precision floating-point arithmetic and use numerical tolerances when reasoning about feasibility and optimality during their search. While…
Recent advancements in Large Language Models (LLMs) have shown remarkable performance across a wide range of tasks. Despite this, the auto-regressive nature of LLM decoding, which generates only a single token per forward propagation, fails…
Semidefinite programs (SDP) are one of the most versatile frameworks in numerical optimization, serving as generalizations of many conic programs and as relaxations of NP-hard combinatorial problems. Their main drawback is their…
A mathematical programming model for a class of single machine family scheduling problem is described in this technical report, with the aim of comparing the performance in solving the scheduling problem by means of mathematical programming…
We give a quantum algorithm for solving semidefinite programs (SDPs). It has worst-case running time $n^{\frac{1}{2}} m^{\frac{1}{2}} s^2 \text{poly}(\log(n), \log(m), R, r, 1/\delta)$, with $n$ and $s$ the dimension and row-sparsity of the…
Operations in areas of importance to society are frequently modeled as Mixed-Integer Linear Programming (MILP) problems. While MILP problems suffer from combinatorial complexity, Lagrangian Relaxation has been a beacon of hope to resolve…
This work focuses on the numerical study of a recently published class of Runge-Kutta methods designed for mixed-precision arithmetic. We employ the methods in solving partial differential equations on modern hardware. In particular we…