{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/visualizing-multidimensional-linear","title":"Visualizing Multidimensional Linear Programming Problems","arxiv_id":"2204.02901","date":"2022-04-06","proceeding":null,"authors":["Nikolay A. Olkhovsky","Leonid B. Sokolinsky"],"abstract":"The article proposes an n-dimensional mathematical model of the visual representation of a linear programming problem. This model makes it possible to use artificial neural networks to solve multidimensional linear optimization problems, the feasible region of which is a bounded non-empty set. To visualize the linear programming problem, an objective hyperplane is introduced, the orientation of which is determined by the gradient of the linear objective function: the gradient is the normal to the objective hyperplane. In the case of searching a maximum, the objective hyperplane is positioned in such a way that the value of the objective function at all its points exceeds the value of the objective function at all points of the feasible region, which is a bounded convex polytope. For an arbitrary point of the objective hyperplane, the objective projection onto the polytope is determined: the closer the objective projection point is to the objective hyperplane, the greater the value of the objective function at this point. Based on the objective hyperplane, a finite regular set of points is constructed, called the receptive field. Using objective projections, an image of a polytope is constructed. This image includes the distances from the receptive points to the corresponding points of the polytope surface. Based on the proposed model, parallel algorithms for visualizing a linear programming problem are constructed. An analytical estimation of its scalability is performed. Information about the software implementation and the results of large-scale computational experiments confirming the efficiency of the proposed approaches are presented.","url_abs":"https://arxiv.org/abs/2204.02901v1","url_pdf":"https://arxiv.org/pdf/2204.02901v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"visualizing-multidimensional-linear","repo_url":"https://github.com/nikolay-olkhovsky/lp-visualization-mpi","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}