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A Space Decomposition-Based Deterministic Algorithm for Solving Linear Optimization Problems

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Departamento de Procesos y Sistemas, Universidad Simón Bolívar, Sartenejas, Baruta, Miranda 1080, Venezuela
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Laboratorio de Evolución, Universidad Simón Bolívar Sartenejas, Baruta, Miranda 1080, Venezuela
Axioms 2019, 8(3), 92; https://doi.org/10.3390/axioms8030092
Received: 1 June 2019 / Revised: 25 July 2019 / Accepted: 26 July 2019 / Published: 1 August 2019
This document introduces a method to solve linear optimization problems. The method’s strategy is based on the bounding condition that each constraint exerts over the dimensions of the problem. The solution of a linear optimization problem is at the intersection of the constraints defining the extreme vertex. The method decomposes the n-dimensional linear problem into n-1 two-dimensional problems. After studying the role of constraints in these two-dimensional problems, we identify the constraints intersecting at the extreme vertex. We then formulate a linear equation system that directly leads to the solution of the optimization problem. The algorithm is remarkably different from previously existing linear programming algorithms in the sense that it does not iterate; it is deterministic. A fully c-sharp-coded algorithm is made available. We believe this algorithm and the methods applied for classifying constraints according to their role open up a useful framework for studying complex linear problems through feasible-space and constraint analysis. View Full-Text
Keywords: linear optimization; deterministic linear optimization algorithm; feasible-space analysis; linear space decomposition linear optimization; deterministic linear optimization algorithm; feasible-space analysis; linear space decomposition
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Febres, G.L. A Space Decomposition-Based Deterministic Algorithm for Solving Linear Optimization Problems. Axioms 2019, 8, 92.

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