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Outer approximation schemes for generalized semi-infinite variational inequality problems

- Burachik, Regina, Lopes, J.

  • Authors: Burachik, Regina , Lopes, J.
  • Date: 2010
  • Type: Text , Journal article
  • Relation: Optimization Vol. 59, no. 4 (2010), p. 601-617
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  • Description: We introduce and analyse outer approximation schemes for solving variational inequality problems in which the constraint set is as in generalized semi-infinite programming. We call these problems generalized semi-infinite variational inequality problems. First, we establish convergence results of our method under standard boundedness assumptions. Second, we use suitable Tikhonov-like regularizations for establishing convergence in the unbounded case.

Nonsmooth Lyapunov pairs for infinite-dimensional first-order differential inclusions

- Adly, Samir, Hantoute, Abderrahim, Théra, Michel

  • Authors: Adly, Samir , Hantoute, Abderrahim , Théra, Michel
  • Date: 2012
  • Type: Text , Journal article
  • Relation: Nonlinear Analysis: Theory, Methods & Applications Vol. 75, no. 3 (February, 2012), p. 985-1008
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  • Description: The main objective of this paper is to provide new explicit criteria to characterize weak lower semicontinuous Lyapunov pairs or functions associated to first-order differential inclusions in Hilbert spaces. These inclusions are governed by a Lipschitzian perturbation of a maximally monotone operator. The dual criteria we give are expressed by means of the proximal and basic subdifferentials of the nominal functions while primal conditions are described in terms of the contingent directional derivative. We also propose a unifying review of many other criteria given in the literature. Our approach is based on advanced tools of variational analysis and generalized differentiation.
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