Publicación: Reducción de variables en la búsqueda de extremos condicionados de funciones multivariantes
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El método tradicional de los multiplicadores u operadores de Lagrange para la resolución de los problemas de extremos condicionados de varias variables, o el de los determinantes jacobianos, son sólo necesarios en presencia de puntos de silla (o de “ensilladura”) o bien cuando la forma implícita de la restricción impide despejar la o las variables que interese substituir en la función objetivo a optimizar. Puede suceder, también, que los expresados métodos no ofrezcan soluciones definitivas y haya que recurrir, justamente, a la técnica referida de reducción o eliminación de variables para solventar eficazmente el problema planteado, como tendremos ocasión de comprobar. Para una mayor claridad del proceso, se desarrollan varios ejercicios representativos y un caso práctico de las ventajas que ofrece la técnica en cuestión.
The traditional method of multipliers or Lagrange’s operators to the resolution of the problems in conditional ends of several variables, or the jacobians determinants, they are only needed in the presence of points of chair (or "tack") either when the implied form of the constraint prevents clear or variables that you want to replace in the objective function to optimize. It can also happen that expressed methods do not provide definitive solutions and have to resort, precisely, to the aforementioned technique of reduction or elimination of variables to effectively solve the problem, as we will have opportunity to see. For greater clarity in the process, develop several representative exercises and a practical case of the advantages offered by the technology in question.
The traditional method of multipliers or Lagrange’s operators to the resolution of the problems in conditional ends of several variables, or the jacobians determinants, they are only needed in the presence of points of chair (or "tack") either when the implied form of the constraint prevents clear or variables that you want to replace in the objective function to optimize. It can also happen that expressed methods do not provide definitive solutions and have to resort, precisely, to the aforementioned technique of reduction or elimination of variables to effectively solve the problem, as we will have opportunity to see. For greater clarity in the process, develop several representative exercises and a practical case of the advantages offered by the technology in question.
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extremos, ecuación condicionante, función objetivo, operador de Lagrange, determinante funcional, variable independiente, punto crítico, ends, determinant equation, objective function, Lagrange’s operator, independent variable, functional determinant, critical point
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