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Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
Graph-based design languages in UML (Unified Modeling Language) are presented as a method to encode and automate the complete design process and the final optimization of the product or complex system. A design language consists of a…
Algorithm NCL is designed for general smooth optimization problems where first and second derivatives are available, including problems whose constraints may not be linearly independent at a solution (i.e., do not satisfy the LICQ). It is…
The rapid evolution of Large Language Models (LLMs) has markedly expanded their application across diverse domains, transforming how complex problems are approached and solved. Initially conceived to predict subsequent words in texts, these…
This material provides thorough tutorials on some optimization techniques frequently used in various engineering disciplines, including convex optimization, linearization techniques and mixed-integer linear programming, robust optimization,…
SMLP: Symbolic Machine Learning Prover an open source tool for exploration and optimization of systems represented by machine learning models. SMLP uses symbolic reasoning for ML model exploration and optimization under verification and…
Spreadsheets provide a flexible and easy to use software development environment, but that leads to error proneness. Work has been done to prevent errors in spreadsheets, including using models to specify distinct parts of a spreadsheet as…
High-quality prompts are crucial for eliciting outstanding performance from large language models (LLMs) on complex tasks. Existing research has explored model-driven strategies for prompt optimization. However, these methods often suffer…
GPUs are popular devices for accelerating scientific calculations. However, as GPU code is usually written in low-level languages, it breaks the abstractions of high-level languages popular with scientific programmers. To overcome this, we…
One of the current trends in robotics is to employ large language models (LLMs) to provide non-predefined command execution and natural human-robot interaction. It is useful to have an environment map together with its language…
We introduce Optimistix: a nonlinear optimisation library built in JAX and Equinox. Optimistix introduces a novel, modular approach for its minimisers and least-squares solvers. This modularity relies on new practical abstractions for…
In this paper, we provide an affirmative answer to the long-standing question: Are GPUs useful in solving linear programming? We present cuPDLP.jl, a GPU implementation of restarted primal-dual hybrid gradient (PDHG) for solving linear…
For complex, high-dimensional Markov Decision Processes (MDPs), it may be necessary to represent the policy with function approximation. A problem is misspecified whenever, the representation cannot express any policy with acceptable…
This paper demonstrates how certified computational tools can be used to address various problems in control theory. In particular, we introduce PACE.jl, a Julia package that implements symbolic elimination techniques, including (among…
This paper introduces HPIPM, a high-performance framework for quadratic programming (QP), designed to provide building blocks to efficiently and reliably solve model predictive control problems. HPIPM currently supports three QP types, and…
Geometric computing with chain complexes allows for the computation of the whole chain of linear spaces and (co)boundary operators generated by a space decomposition into a cell complex. The space decomposition is stored and handled with…
Scientific computing is increasingly incorporating the advancements in machine learning and the ability to work with large amounts of data. At the same time, machine learning models are becoming increasingly sophisticated and exhibit many…
Prompt optimization has become crucial for enhancing the performance of large language models (LLMs) across a broad range of tasks. Although many research papers demonstrate its effectiveness, practical adoption is hindered because existing…
Existing benchmarks for evaluating mathematical reasoning in large language models (LLMs) rely primarily on competition problems, formal proofs, or artificially challenging questions -- failing to capture the nature of mathematics…
Optimization models have been applied to solve a wide variety of decision-making problems. These models are usually developed by optimization experts but are used by practitioners without optimization expertise in various application…