Linear Spaces and Gâteaux Variations

  • John L. Troutman
Part of the Undergraduate Texts in Mathematics book series (UTM)


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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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • John L. Troutman
    • 1
  1. 1.Department of MathematicsSyracuse UniversitySyracuseUSA

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