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Critical multipliers in variational systems via second-order generalized differentiation. (English) Zbl 1407.90314
The following equation system is studied: $\Psi(x,v) = 0, \;\;v \in \partial\theta(\Phi),$ where $$\Phi: \mathbb R^n \longrightarrow \mathbb R^m$$, $$\Psi : \mathbb R^n \times \mathbb R^m \longrightarrow \mathbb R^l$$, $$\theta: \mathbb R^m \longrightarrow \overline{\mathbb R}$$ is an extended real-valued function, $$\partial$$ denotes an appropriate subdifferential. The authors use mainly a convex function $$\theta$$ so that $$\partial$$ is the classical subdifferential.
The authors introduce the notion of critical and non-critical mulltipliers for the variational system. A complete general characterization of the critical and non-critical multipliers is obtained. Especially comprehensive results are presented for the case that $$\theta$$ belongs to the class of convex piecewise linear functions.

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