Robust saddle‐point criterion in second‐order partial differential equation and partial differential inequation constrained control problems
Savin Treanţă
Abstract
Abstract In this article, for a given class of multi‐dimensional scalar variational control problems (named ) with mixed constraints implying second‐order partial differential equations and inequations, we introduce an auxiliary (modified) class of variational control problems (named ), which is much easier to study, and provide some characterization results of and by using the notions of normal weak robust optimal solution and robust saddle‐point associated with a Lagrange functional corresponding to . For this aim, we consider scalar multiple integral cost functionals and the notion of convexity associated with a multiple integral functional driven by an uncertain multi‐time controlled second‐order Lagrangian.
Topics & Concepts
Saddle pointMathematicsScalar (mathematics)ConvexityPartial differential equationApplied mathematicsPartial derivativeLagrange multiplierFirst-order partial differential equationSaddleClass (philosophy)Mathematical optimizationMathematical analysisComputer scienceGeometryArtificial intelligenceFinancial economicsEconomicsOptimization and Variational AnalysisContact Mechanics and Variational InequalitiesNonlinear Differential Equations Analysis