The General Concept of Cone Approximations in Nondifferentiable Optimization
General optimization problems connected with necessary conditions for optimality have been studied by many authors in recent years. Since Clarke (1975) introduced the notion of a generalized gradient and the corresponding tangent cone, numerous papers have been published which extend standard smooth and convex optimization results to the general case.
KeywordsLocal Solution Directional Derivative Tangent Cone Slater Condition Nondifferentiable Optimization
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- Abadie, J. (1967). On the Kuhn/Tucker theorem. In: J. Abadie (ed.): Nonlinear Programming. North-Holland, Amsterdam, pp. 17–36.Google Scholar
- Clarke, F. (1983). Optimization and Nonsmooth Analysis. John Wiley, New York.Google Scholar
- Dubovitskij, A.J. and Miljutin, A.A. (1965). Extremum problems under constraints (in Russian). Vychisl. Mat. i Mat. Fiz., 5: 395–453.Google Scholar
- Elster, K.-H. and Thierfelder, J. Abstract cone approximations and generalized differentiability in nonsmooth optimization. (Forthcoming).Google Scholar
- Ioffe, A.D. and Tikhomirov, V.M. (1979). Theorie der Extremalaufgaben. DVW Berlin.Google Scholar
- Rockafellar, R.T. (1981). The Theory of Subgradients and its Applications in Problems of Optimization. HeldermannVerlag, Berlin.Google Scholar
- Thierfelder, J. (1984). Beiträge zur Theorie der nichtglatten Optimierung. Diss. A, TH Ilmenau.Google Scholar