Calmness as a Constraint Qualification for M-Stationarity Conditions in MPECs
Mathematical programs with equilibrium constraints (MPECs) represent an important class of nonlinear optimization problems. Due to their constraint set being defined as the solution of some parameter-dependent generalized equation, the application of standard constraint qualifications (CQs) from nonlinear programming to MPECs is not straightforward. Rather than turning MPECs into mathematical programs with complementarity constraints (MPCCs) and applying specially adapted CQs, we want to present here a variational-analytic approach to dual stationarity conditions for MPECs on the basis of Lipschitzian properties of the perturbed generalized equation. The focus will be on the so-called calmness property, ensuring an appropriate calculus rule for the Mordukhovich normal cone.
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