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We observe a disconnect between the developers and the end users of linear algebra libraries. On the one hand, the numerical linear algebra and the high-performance communities invest significant effort in the development and optimization…
Operations research (OR) uses mathematical models to enhance decision-making, but developing these models requires expert knowledge and can be time-consuming. Automated mathematical programming (AMP) has emerged to simplify this process,…
This paper introduces SOLID (Synergizing Optimization and Large Language Models for Intelligent Decision-Making), a novel framework that integrates mathematical optimization with the contextual capabilities of large language models (LLMs).…
We present the Julia interface Polymake.jl to polymake, a software for research in polyhedral geometry. We describe the technical design and how the integration into Julia makes it possible to combine polymake with state-of-the-art…
The immense evolution in Large Language Models (LLMs) has underscored the importance of massive, heterogeneous, and high-quality data. A data recipe is a mixture of data from different sources for training LLMs, which plays a vital role in…
Quantum parameter estimation promises a high-precision measurement in theory, however, how to design the optimal scheme in a specific scenario, especially under a practical condition, is still a serious problem that needs to be solved case…
The widespread adoption of large language models such as ChatGPT and Bard has led to unprecedented demand for these technologies. The burgeoning cost of inference for ever-increasing model sizes coupled with hardware shortages has limited…
Combinatorial optimization (CO) problems, central to operation research and theoretical computer science, present significant computational challenges due to their NP-hard nature. While large language models (LLMs) have emerged as promising…
Our aim is to explain mathematical programs with equilibrium constraints (MPECs), motivate them through applications, present the main equivalent formulations of equilibrium constraints, and summarize the basic existence theory for optimal…
Numerous real-world decision-making problems can be formulated and solved using Mixed-Integer Linear Programming (MILP) models. However, the transformation of these problems into MILP models heavily relies on expertise in operations…
Large language models (LLMs) present intriguing opportunities to enhance user interaction with traditional algorithms and tools in real-world applications. An advanced planning system (APS) is a sophisticated software that leverages…
This paper introduces OptimizedDP, a high-performance software library for several common grid-based dynamic programming (DP) algorithms used in control theory and robotics. Specifically, OptimizedDP provides functions to numerically solve…
We discuss the use of both MPI and OpenMP in the teaching of senior undergraduate and junior graduate classes in parallel programming. We briefly introduce the OpenMP standard and discuss why we have chosen to use it in parallel programming…
Large language models (LLMs) have recently shown strong reasoning capabilities beyond traditional language tasks, motivating their use for numerical optimization. This paper presents LLMize, an open-source Python framework that enables…
Joint object matching, also known as multi-image matching, namely, the problem of finding consistent partial maps among all pairs of objects within a collection, is a crucial task in many areas of computer vision. This problem subsumes…
Business Process Management (BPM) aims to improve organizational activities and their outcomes by managing the underlying processes. To achieve this, it is often necessary to consider information from various sources, including unstructured…
Mathematical reasoning serves as a cornerstone for assessing the fundamental cognitive capabilities of human intelligence. In recent times, there has been a notable surge in the development of Large Language Models (LLMs) geared towards the…
Programming language modeling has attracted extensive attention in recent years, and it plays an essential role in program processing fields. Statistical language models, which are initially designed for natural languages, have been…
We introduce the language QML, a functional language for quantum computations on finite types. Its design is guided by its categorical semantics: QML programs are interpreted by morphisms in the category FQC of finite quantum computations,…
Large language models (LLMs) still grapple with complex tasks like mathematical reasoning. Despite significant efforts invested in improving prefix prompts or reasoning process, the crucial role of problem context might have been neglected.…