An augmented Lagrangian method for quasi-equilibrium problems. (English) Zbl 1446.90154
Summary: In this paper, we propose an Augmented Lagrangian algorithm for solving a general class of possible non-convex problems called quasi-equilibrium problems (QEPs). We define an Augmented Lagrangian bifunction associated with QEPs, introduce a secondary QEP as a measure of infeasibility and we discuss several special classes of QEPs within our theoretical framework. For obtaining global convergence under a new weak constraint qualification, we extend the notion of an Approximate Karush-Kuhn-Tucker (AKKT) point for QEPs (AKKT-QEP), showing that in general it is not necessarily satisfied at a solution, differently from its counterpart in optimization. We study some particular cases where AKKT-QEP does hold at a solution, while discussing the solvability of the subproblems of the algorithm. We also present illustrative numerical experiments.
MSC:
| 90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |
Keywords:
augmented Lagrangian methods; quasi-equilibrium problems; equilibrium problems; constraint qualifications; approximate-KKT conditionsSoftware:
ALGENCANReferences:
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