TL;DR
This paper introduces a novel n-dimensional visualization model for linear programming problems using artificial neural networks, enabling better understanding and solving of multidimensional optimization tasks.
Contribution
It presents a new mathematical model for visualizing multidimensional linear programming problems and develops parallel algorithms for their visualization and solution.
Findings
Effective visualization of high-dimensional LP problems achieved
Parallel algorithms demonstrate scalability and efficiency
Software implementation validated through large-scale experiments
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:…
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