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Optimisation non différentiable

Optimisation non différentiable. Ce chapitre est consacré aux méthodes de type sous-gradient pour résoudre des problèmes de programmation mathématique où la fonction économique n’est pas différentiable en tout point.

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Optimisation non différentiable

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  1. Optimisation non différentiable

  2. Ce chapitre est consacré aux méthodes de type sous-gradient pour résoudre des problèmes de programmation mathématique où la fonction économique n’est pas différentiable en tout point. • Les sous-gradients tiennent la place qu’occupe les gradients lorsque la fonction économique est différentiable.

  3. Méthode du sous-gradient

  4. Direction opposée au sous-gradient

  5. Condition d’optimalité

  6. Choix du pas tk

  7. Dual Ascent Method

  8. Références [1]Polyak B.T. (1967), A General Method of Solving Extremum Problems, Soviet Mathematics Doklady 8, 593-597. [2] Held M., Wolfe P., Crouwder H.P. (1974), Validation of Subgradient Optimization’ Mathematical Programming 6, 62-88. [3] Goffin J.L. (1977), On Convergence Rates of Subgradient Optimization Methods, Mathematical Programming 13, 329-347. [4] Shor N.Z. (1970), Convergence Rtae of the Gradient Descent Method with Dilatation of the Space, Cybernatic 6, 102-108. [5] Lemaréchal C. (1978), Nonsmooth Optimization and Descent Methods’ International Institute for Applied Systems Analysis, Research Report 78-4, Laxenburg, Austria [6] Minoux M. (1993), Programmation Mathématique, Théorie et Algorithmes, Dunod, Paris. [7] Balakrishnan A., Magnanti T.L., Wong R.T., (1989) A Dual-Ascent Procedure for Large-Scale Uncapacitated Network Design, Operations Research 37, 716-740.

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