Journal of Global Optimization

, Volume 22, Issue 1–4, pp 119–136 | Cite as

Convergence analysis of non-quadratic proximal methods for variational inequalities in Hilbert spaces

  • Alexander Kaplan
  • Rainer TichatschkeEmail author


We consider a general approach for the convergence analysis of proximal-like methods for solving variational inequalities with maximal monotone operators in a Hilbert space. It proves to be that the conditions on the choice of a non-quadratic distance functional depend on the geometrical properties of the operator in the variational inequality, and –- in particular –- a standard assumption on the strict convexity of the kernel of the distance functional can be weakened if this operator possesses a certain `reserve of monotonicity'. A successive approximation of the `feasible set' is performed, and the arising auxiliary problems are solved approximately. Weak convergence of the proximal iterates to a solution of the original problem is proved.

Variational inequalities Monotone operators Proximal point methods Regularization 


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© Kluwer Academic Publishers 2002

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TrierTrierGermany

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