Abstract
We describe in this article a scheme of necessary conditons for variational problems which are devoid of the customary smoothness and convexity assumptions. This is a descriptive paper based upon the author’s dissertation [1]. Proofs are omitted here; they will appear elsewhere.
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References
F.H. Clarke, Necessary Conditions for Nonsmooth Problems in Optimal Control and the Calculus of Variations, thesis, University of Washington (1973).
H. Halkin, Extremal Properties of Biconvex Contingent Equations in “Ordinary Differential Equations” (NRL-MRC Conference), Academic Press (1972).
E. Polak, An Historical Survey of Computational Methods in Optimal Control, SIAM Review 15 (1973), 553–576.
R.T. Rockafellar, Conjugate Convex Functions in Optimal Control and the Calculus of Variations, J. Math. Anal. Appl. 32 (1970), 174–222.
R.T. Rockafellar, Existence and Duality Theorems for Convex Problems of Bolza, Trans. A.M.S. 159 (1971), 1–39.
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© 1974 Springer-Verlag Berlin · Heidelberg
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Clarke, F.H. (1974). Necessary Conditions for Nonsmooth Variational Problems. In: Kirby, B.J. (eds) Optimal Control Theory and its Applications. Lecture Notes in Economics and Mathematical Systems, vol 106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48290-8_5
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DOI: https://doi.org/10.1007/978-3-642-48290-8_5
Publisher Name: Springer, Berlin, Heidelberg
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