Abstract
Each problem considered previously reduces to that of optimizing (usually minimizing) a real valued function J defined on a subset D of a linear space Y. In the present chapter we shall view problems in this context and introduce the associated directional derivatives (Gâteaux variations) of the functions which will be required for what follows. We begin with a catalogue of standard linear spaces presupposing some familiarity with vector space operations, with continuity, and with differentiability in ℝd.
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© 1996 Springer Science+Business Media New York
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Troutman, J.L. (1996). Linear Spaces and Gâteaux Variations. In: Variational Calculus and Optimal Control. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0737-5_3
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DOI: https://doi.org/10.1007/978-1-4612-0737-5_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6887-1
Online ISBN: 978-1-4612-0737-5
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