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2 results

  • When some variational properties forceconvexity

  • M. Volle, J.-B. Hiriart-Urruty, C. Zălinescu
  • Journal:
    ESAIM: Control, Optimisation and Calculus of Variations / Volume 19 / Issue 3 / July 2013
    Published online by Cambridge University Press:
    17 May 2013, pp. 701-709
    Print publication:
    July 2013

  • The notion of adequate (resp. strongly adequate) function has been recently introduced tocharacterize the essentially strictly convex (resp. essentially firmly subdifferentiable)functions among the weakly lower semicontinuous (resp. lower semicontinuous) ones. In thispaper we provide various necessary and sufficient conditions in order that the lowersemicontinuous hull of an extended real-valued function on a reflexive Banach space isessentially strictly convex. Some new results on nearest (farthest) points are derivedfrom this approach.

  • A General Formula on the Conjugate of the Difference of Functions

  • J.-B. Hiriart-Urruty
  • Journal:
    Canadian Mathematical Bulletin / Volume 29 / Issue 4 / 01 December 1986
    Published online by Cambridge University Press:
    20 November 2018, pp. 482-485
    Print publication:
    01 December 1986
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  • Given an arbitrary function g :X→ (-∞, +∞] and a lowersemicontinuous convex function h:X→ (-∞, +∞], we give the general expression of the conjugate (g — h)* of g - h in terms of g* and h* . As a consequence, we get Toland's duality theorem: