Optimal Obstacle Control Problems Involving Nonsmooth Cost Functionals and Quasilinear Variational Inequalities
Zijia Peng
Abstract
This paper deals with the optimal control of an obstacle problem where the control variable is the obstacle. The state system is described by a class of quasilinear elliptic variational inequalities with nonmonotone and nonsmooth perturbations. The cost functional is neither smooth nor convex, but locally Lipschitz continuous. The existence and approximation result of optimal solutions are proved. The optimality system is derived by Lagrange multiplier rules, smooth approximations, and nonsmooth analysis techniques.
Topics & Concepts
Variational inequalityMathematicsLipschitz continuityObstacle problemObstacleLagrange multiplierOptimal controlRegular polygonClass (philosophy)Applied mathematicsVariational analysisMathematical optimizationMathematical analysisComputer scienceGeometryLawArtificial intelligencePolitical scienceContact Mechanics and Variational InequalitiesOptimization and Variational AnalysisNonlinear Partial Differential Equations