Solución de un problema cuadrático entero usando una generalización del método de Fiedler
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Date
2024
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Universidad Nacional de Trujillo
Abstract
En el presente trabajo se soluciona un problema cuadrático entero, el cual se transforma o relaja a un problema cuadrático binario, garantizando la existencia y optimalidad de su solución mediante la demostración de dos teoremas. El problema cuadrático binario se puede representar como un problema de partición de un grafo, para la solución de este problema se generaliza el método de Fiedler para grafos ponderados, definiendo una matriz laplaciana para un grafo ponderado de donde se obtienen el valor y vector de Fiedler que permiten hallar la partición del grafo y así obtener la solución del problema cuadrático entero
Abstract In the present work an integer quadratic problem is solved, which is transformed or relaxed to a binary quadratic problem, guaranteeing the existence and optimality of its solution by means of the proof of two theorems. The binary quadratic problem can be represented as a partition problem of a graph, for the solution of this problem the Fiedler method for weighted graphs is generalized, defining a Laplacian matrix for a weighted graph from which the Fiedler value and vector that allow finding the partition of the graph and thus obtaining the solution of the integer quadratic problem are obtained
Abstract In the present work an integer quadratic problem is solved, which is transformed or relaxed to a binary quadratic problem, guaranteeing the existence and optimality of its solution by means of the proof of two theorems. The binary quadratic problem can be represented as a partition problem of a graph, for the solution of this problem the Fiedler method for weighted graphs is generalized, defining a Laplacian matrix for a weighted graph from which the Fiedler value and vector that allow finding the partition of the graph and thus obtaining the solution of the integer quadratic problem are obtained
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Keywords
Grafo ponderado, Matriz Laplaciana, Método de Fiedler, valor
y vector de Fiedler