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Strong stationarity for optimal control of variational inequalities of the second kind. (English) Zbl 1502.49008

Hintermüller, Michael (ed.) et al., Non-smooth and complementarity-based distributed parameter systems. Simulation and hierarchical optimization. Cham: Birkhäuser. ISNM, Int. Ser. Numer. Math. 172, 307-327 (2022).
Summary: This chapter is concerned with necessary optimality conditions for optimal control problems governed by variational inequalities of the second kind. The so-called strong stationarity conditions are derived in an abstract framework. Strong stationarity conditions are regarded as the most rigorous ones, since they imply all other types of stationarity concepts and are equivalent to purely primal optimality conditions. The abstract framework is afterward applied to four application-driven examples.
For the entire collection see [Zbl 1481.49002].

MSC:

49J40 Variational inequalities
49Q12 Sensitivity analysis for optimization problems on manifolds
49K27 Optimality conditions for problems in abstract spaces
35J86 Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic operators
90C31 Sensitivity, stability, parametric optimization
49J27 Existence theories for problems in abstract spaces
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