Herzog, Roland; Meyer, Christian; Wachsmuth, Gerd B- and strong stationarity for optimal control of static plasticity with hardening. (English) Zbl 1266.49013 SIAM J. Optim. 23, No. 1, 321-352 (2013). Summary: Optimal control problems for the variational inequality of static elastoplasticity with linear kinematic hardening are considered. The control-to-state map is shown to be weakly directionally differentiable, and local optimal controls are proved to verify an optimality system of B-stationary type. For a modified problem, local minimizers are shown to even satisfy an optimality system of strongly stationary type. Cited in 31 Documents MSC: 49J40 Variational inequalities 70Q05 Control of mechanical systems 74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) 35R45 Partial differential inequalities and systems of partial differential inequalities Keywords:mathematical programs; complementarity constraints; function space; variational inequalities of first kind; elastoplasticity; Bouligand stationarity; strong stationarity PDFBibTeX XMLCite \textit{R. Herzog} et al., SIAM J. Optim. 23, No. 1, 321--352 (2013; Zbl 1266.49013) Full Text: DOI