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In the Model-Driven Software Engineering (MDSE) community, the combination of techniques operating on graph-based models (e.g., Pattern Matching (PM) and Graph Transformation (GT)) and Integer Linear Programming (ILP) is a common…
Large Language Models (LLMs) are increasingly being adopted as tools for learning; however, most tools remain text-only, limiting their usefulness for domains where visualizations are essential, such as mathematics. Recent work shows that…
Linear operators and optimisation are at the core of many algorithms used in signal and image processing, remote sensing, and inverse problems. For small to medium-scale problems, existing software packages (e.g., MATLAB, Python numpy and…
Mixed-integer linear programming (MILP) is widely employed for modeling combinatorial optimization problems. In practice, similar MILP instances with only coefficient variations are routinely solved, and machine learning (ML) algorithms are…
Geometric Algebra (GA) presents challenges to learners due to its highly abstract mathematical structure and complex operational rules, as translating algebraic manipulations into concrete geometric interpretations is a non-intuitive…
Non-programming users should be able to create their own customized scripts to perform computer-based tasks for them, just by demonstrating to the machine how it's done. To that end, we develop a system prototype which…
Graph self-supervised learning (GSSL) has emerged as a compelling framework for extracting informative representations from graph-structured data without extensive reliance on labeled inputs. In this study, we introduce Graph Interplay…
Object categories are typically organized into a multi-granularity taxonomic hierarchy. When classifying categories at different hierarchy levels, traditional uni-modal approaches focus primarily on image features, revealing limitations in…
The area of geometry with its very strong and appealing visual contents and its also strong and appealing connection between the visual content and its formal specification, is an area where computational tools can enhance, in a significant…
We present a novel relaxation framework for general mixed-integer nonlinear programming (MINLP) grounded in computational geometry. Our approach constructs polyhedral relaxations by convexifying finite sets of strategically chosen points,…
Much research has highlighted the impressive capabilities of large language models (LLMs), like GPT and Bard, for solving introductory programming exercises. Recent work has shown that LLMs can effectively solve a range of more complex…
Dantzig's vertex pivot simplex method has been published for more than seven decades. Amazingly, it remains one of the most efficient methods to solve linear programming (LP) problem after numerous efforts trying to find some better…
Navigating rigid body objects through crowded environments can be challenging, especially when narrow passages are presented. Existing sampling-based planners and optimization-based methods like mixed integer linear programming (MILP)…
In many learning settings, it is beneficial to augment the main features with pairwise interactions. Such interaction models can be often enhanced by performing variable selection under the so-called strong hierarchy constraint: an…
Spatial reasoning in 3D scenes requires precise geometric calculations that challenge vision-language models. Visual programming addresses this by decomposing problems into steps calling specialized tools, yet existing methods rely on…
Replicability in machine learning (ML) research is increasingly concerning due to the utilization of complex non-deterministic algorithms and the dependence on numerous hyper-parameter choices, such as model architecture and training…
We expand the basic geometric elements of the simplex method to linear programs in locally convex topological vector spaces and provide conditions under which the method converges in value to optimality. This setting generalizes many…
The Simplex tableau has been broadly used and investigated in the industry and academia. With the advent of the big data era, ever larger problems are posed to be solved in ever larger machines whose architecture type did not exist in the…
We present PDLP, a practical first-order method for linear programming (LP) designed to solve large-scale LP problems. PDLP is based on the primal-dual hybrid gradient (PDHG) method applied to the minimax formulation of LP. PDLP…
Mixed integer nonlinear programming (MINLP) problems are encountered in modeling a physical/industrial process consisting both nonlinearity and discrete selective parameters. There are variety of algorithms for solving MINLP problems most…