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Graphical derivatives and stability analysis for parameterized equilibria with conic constraints. (English) Zbl 1330.49013
Summary: The paper concerns parameterized equilibria governed by generalized equations whose multivalued parts are modeled via regular normals to nonconvex conic constraints. Our main goal is to derive a precise pointwise second-order formula for calculating the graphical derivative of the solution maps to such generalized equations that involves Lagrange multipliers of the corresponding KKT systems and critical cone directions. Then, we apply the obtained formula to characterizing a Lipschitzian stability notion for the solution maps that is known as isolated calmness.

MSC:
49J53 Set-valued and variational analysis
49J52 Nonsmooth analysis
49K40 Sensitivity, stability, well-posedness
90C31 Sensitivity, stability, parametric optimization
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