Abstract
We give some ideas which lead to descent methods for minimizing nondifferentiable functions. Such methods have been published in several papers and they all involve the same concept, namely the ε — subdifferential.
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References
D.P.Bertsekas,S.K.Mitter: A descent numerical method for optimization problems with nondifferentiable cost functionals. SIAM Journal on Control Vol 11 n°4 (1973) PP 637–652.
V.F.Temjanov: Algorithms for some minimax problems. Journal of Computer and Systems Science Vol 2 (1968) PP 342–380.
H.Everett III: Generalized Multipliers Method for solving problems of allocation of Resources. Operations Research Vol 11 (1963) PP 399–417.
C.Lemarechal: An Algorithm for Minimizing Convex Functions. Proceedings IFIP Congress (Stockholm, 1974) North Holland Publishing Company pp 552–556
C.Lemarechal: Minimization of Nondifferentiable Functions with Constraints Proceedings 12th Conference on Circuit Theory (Allerton, 1974) The University of Illinois at Urbana Champaign pp 16–24.
C.Lemarechal: Nondifferentiable Programming and GLM technique, Application to a Nonconvex Programming Problem. Working Paper IRIA-Laboria France.
C.Lemarechal: An Extension of “Davidon” Methods to nondifferentiable problems. Mathematical Programming Study n°3 (to appear) North Holland Publishing Company.
G.P.Mc Cormick,K.Ritter: Projection Method for Unconstrained Optimization. Journal of Optimization Theory and Applications Vol 10 n°2 (1972) pp 57–66.
R.T.Rockafellar: Convex Analysis. Princeton University Press, Princeton (1970)
K.Ritter: A Method of Conjugate Directions for Linearly Constrained Nonlinear Programming Problems. SIAM Journal on Numerical Analysis Vol 12 n°3 (1975) pp 273–303.
P.Wolfe: Finding the Nearest Point in a Polytope. Mathematical Prograici.ing Study n°1 (to appear) North Holland Publishing Company
P.Wolfe: A Method of Conjugate Subgradients for Minimizing Nondifferentiable Functions. Proceedings, Allerton Conference (See[5]).
P.Wolfe: A Method of Conjugate Subgradients for Minimizing Nondifferentiable Functions. Nonlinear Programming Study n°3 (See [7])
G.Zoutendijk: Methods of Feasible Directions. Elsevier, Amsterdam (1960)
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© 1976 Springer-Verlag Berlin · Heidelberg
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Lemarechal, C. (1976). Nondifferentiable Optimisation Subgradient and ε — Subgradient Methods. In: Oettli, W., Ritter, K. (eds) Optimization and Operations Research. Lecture Notes in Economics and Mathematical Systems, vol 117. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46329-7_17
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DOI: https://doi.org/10.1007/978-3-642-46329-7_17
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