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Optimality conditions for optimal control problems of variational inequalities. (English) Zbl 0627.49011
Control problems for systems described by partial differential equations and applications, Proc. IFIP-WG 7.2 Work. Conf., Gainesville/Fla. 1986, Lect. Notes Control Inf. Sci. 97, 143-153 (1987).
[For the entire collection see Zbl 0619.00014.]
An optimal control problem governed by an elliptic variational inequality is transformed into a minimization problem, in which the functional to be minimized is convex along two special directions. By using these facts the authors derive some optimality condition for the optimal control and suggest an algorithm for the numerical solution of the problem. The state variational inequality is similar to that modelling the elastic-plastic torsion of a cylindrical bar.
Reviewer: P.Quittner

MSC:
49K20 Optimality conditions for problems involving partial differential equations
35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000)
49M05 Numerical methods based on necessary conditions
49J40 Variational inequalities
49M20 Numerical methods of relaxation type