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Solving quasi-variational inequalities via their KKT conditions. (English) Zbl 1293.65100
The authors propose a totally different approach to the solution of quasi-variational inequalities (QVIs). Assuming that the feasible set mapping \(K(\cdot)\) is described by a finite number of parametric inequalities, the Karush-Kuhn-Tucker (KKT) conditions of the QVI is reformulated then as a system of constrained equations, and then an interior-point method is applied. Main result: The authors propose and analyze a globally convergent algorithm for the solution of a finite-dimensional QVI. The convergence is established for a wide array of different classes of problems including QVIs with the feasible set given by moving sets, linear systems with variable right-hand sides, box constraints with variable bounds, and bilinear constraints. These results surpass by far existing convergence analyses, the latter all having a somewhat limited scope. The results in this paper constitute an important step towards the development of theoretically reliable and numerically efficient methods for the solution of QVIs.

65K15 Numerical methods for variational inequalities and related problems
49J40 Variational inequalities
49M37 Numerical methods based on nonlinear programming
90C51 Interior-point methods
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