Pontryagin's principle in the control of semilinear elliptic variational inequalities

Relaxation of optimal control problems coercive in L P -spaces

“…The above outlined example reproduces (and sometimes generalizes) standard results, e.g. by Alibert and Raymond (preprint), Bonnans and Casas (1991, 1992, Bonnans and Tiba (1991), Casas (1993,to appear), Casas and Fernandez (1991), Mackenroth (1986, Raitums (1986)], or Zolezzi (1972) where only scalar case (i.e. n = 1) has been considered without any relaxation, i.e.…”

Optimal Control Problems for Parabolic Hemivariational Inequalities With Boundary Conditions

“…We refer to [11,18] to see the applications of nonlinear variational inequalities. First order necessary conditions for state constraint optimal control problems governed by semilinear elliptic problems have been obtained by Bonnans and Tida [6] using methods of convex analysis (see also [12]). …”

B- and Strong Stationarity for Optimal Control of Static Plasticity with Hardening

“…In contrast to the multitude of papers concerning regularization and C-stationarity conditions for infinite dimensional MPECs, see e.g., Friedman [1986], Bonnans and Tiba [1991], Bergounioux [1997], Bergounioux [1998], Bergounioux and Zidani [1999], Kunisch [2000, 2010], Hintermüller [2001Hintermüller [ , 2008, , , Zhu [2006], Farshbaf-Shaker [2011], there are fewer contributions which address the question of stricter optimality conditions. We refer to the classical paper of Mignot and Puel [1984], where the obstacle problem is discussed.…”