Approximating optimal control problems governed by variational inequalities

Abstract

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Sufficient optimality conditions and semi-smooth newton methods for optimal control of stationary variational inequalities

“…In this respect the literature essentially offers two approaches. One is based on convex analysis techniques, see for instance [16], the other one on approximation methods, we refer to [1,12], and further references given there. The main concern here is to obtain a system of conditions as complete as possible, so that its solutions in turn provide the solution to (P), see e.g.…”

Optimal control of variational inequalities: A mathematical programming approach

“…Our purpose is to give some optimality conditions that can be easily exploited numerically. These kind of problems have been extensively studied by many authors, as for example Barbu (1984), Mignot and Puel (1984) or Friedman (1982Friedman ( ,1986. Let us present the problem we are interested in more precisely now.…”

“…Moreover, as we want to focus on the solution (Ya, Va, ea); so, following Barbu (1984), we add some adapted penalization terms to the functional J. From now, a> 0 is fixed; so we omit the index a for convenience (when no confusion is possible).…”

Pontryagin's maximum principle for optimal control of a non-well-posed parabolic differential equation involving a state constraint

“…In the memorial work of Lions [5], linear optimal control theory for distributed parameter systems was developed to a considerable extent by using fundamental results on the existence and regularity of solutions to linear partial differential equations. Barbu [1,2] contributed greatly to optimal control theory for nonlinear systems. The theory of nonlinear accretive operators and of nonlinear differential equations of accretive type has occupied an important place among functional methods in the theory of nonlinear partial differential equations since its inception in the 1960s.…”