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Minimization of Convex Functions

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

Abstract

By utilizing the Gâteaux variations from the preceding chapter, it is straightforward to characterize convexity for a function J on a subset D of a linear space Y, such that a convex function is automatically minimized by a yD at which its Gâteaux variations vanish.1 Moreover, in the presence of strict convexity, there can be at most one such y. A large and useful class of functions is shown to be convex. In particular, in §3.2, the role of [strongly] convex integrands f in producing [strictly] convex integral functions F is examined, and a supply of such f is made accessible through the techniques and examples of §3.3. Moreover, the Gâteaux variations of integral functions will, in general, vanish at each solution y of an associated differential equation (of Euler-Lagrange).

Keywords

Convex Function Minimal Surface Integral Function Strict Convexity Convex Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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