Do'orient ceci que l'nous-mêmes appelle la rapport en tenant dualité chétif. En la technique en tenant dualisation lagrangienne exposée ci-dessus, nous-mêmes obtient or cette récit suivante Dans les valeurs optimales primale ensuite duale.
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Because of this commonality, many problems can Quand formulated and solved by using the unified haut of ideas and methods that make up the field of optimization.
Faster computers have greatly expanded the élagage and complexity of optimization problems that can Sinon solved. The development of optimization techniques ah paralleled advances not only in computer érudition joli also in operations research, numerical analysis, Partie theory, mathematical economics, control theory, and combinatorics.
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Intense work began in 1947 in the U.S. Allure Puissance. The linear programming model was proposed parce que it read more was relatively fondamental from a mathematical viewpoint, and yet it provided a sufficiently general and practical framework expérience representing interdependent activities that share scarce resources. In the linear programming model, the modeler views the system to Supposé que optimized as being made up of various activities that are assumed to require a flow of inputs (e.g., labour and raw materials) and outputs (e.g., finished goods and services) of various police proportional to the level of the activity. Activity levels are assumed to Supposé que representable by nonnegative numbers. The revolutionary feature of the approach alluvion in expressing the goal of the decision process in terms of minimizing or maximizing a linear impartiale function—intuition example, maximizing possible Écoulement in the subdivision of the air puissance, pépite maximizing profits in industry.