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Note on the paper: interior proximal method for variational inequalities on non-polyhedral sets

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Kaplan A., Tichatschke R.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2010
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tom 30
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nr 1
51-59
EN
In this paper we clarify that the interior proximal method developed in [6] (vol. 27 of this journal) for solving variational inequalities with monotone operators converges under essentially weaker conditions concerning the functions describing the "feasible" set as well as the operator of the variational inequality.
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Interior proximal method for variational inequalities on non-polyhedral sets

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Kaplan A., Tichatschke R.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2007
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tom 27
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nr 1
71-93
EN
Interior proximal methods for variational inequalities are, in fact, designed to handle problems on polyhedral convex sets or balls, only. Using a slightly modified concept of Bregman functions, we suggest an interior proximal method for solving variational inequalities (with maximal monotone operators) on convex, in general non-polyhedral sets, including in particular the case in which the set is described by a system of linear as well as strictly convex constraints. The convergence analysis of the method studied admits the use of the 𝝐-enlargement of the operator and an inexact solution of the subproblems.
3
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On a regularization method for variational inequalities with P_0 mappings

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Konnov I., Mazurkevich E., Ali M.
International Journal of Applied Mathematics and Computer Science
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2005
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tom 15
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nr 1
35-44
EN
We consider partial Browder-Tikhonov regularization techniques for variational inequality problems with P_0 cost mappings and box-constrained feasible sets. We present classes of economic equilibrium problems which satisfy such assumptions and propose a regularization method for these problems.
4
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On minimizing noncoercive functionals on weakly vlosed sets

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Le V. K., Schmitt K.
Banach Center Publications
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1996
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tom 35
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nr 1
51-72
EN
We consider noncoercive functionals on a reflexive Banach space and establish minimization theorems for such functionals on smooth constraint manifolds. The functionals considered belong to a class which includes semi-coercive, compact-coercive and P-coercive functionals. Some applications to nonlinear partial differential equations are given.
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