Search results for " viscosity solution"

showing 4 items of 4 documents

Objective function design for robust optimality of linear control under state-constraints and uncertainty

2009

We consider a model for the control of a linear network flow system with unknown but bounded demand and polytopic bounds on controlled flows. We are interested in the problem of finding a suitable objective function that makes robust optimal the policy represented by the so-called linear saturated feedback control. We regard the problem as a suitable differential game with switching cost and study it in the framework of the viscosity solutions theory for Bellman and Isaacs equations. © 2009 EDP Sciences, SMAI.

Flow control (data)Mathematical optimizationControl and OptimizationControl (management)State (functional analysis)Optimal control viscosity solutions differential games switching flow control networksOptimal controlComputational MathematicsControl and Systems EngineeringControl theoryViscosity (programming)Bounded functionDifferential gameMathematicsLinear control
researchProduct

Robust optimality of linear saturated control in uncertain linear network flows

2008

We propose a novel approach that, given a linear saturated feedback control policy, asks for the objective function that makes robust optimal such a policy. The approach is specialized to a linear network flow system with unknown but bounded demand and politopic bounds on controlled flows. All results are derived via the Hamilton-Jacobi-Isaacs and viscosity theory.

Inventory controlMathematical optimizationControl theoryViscosity (programming)Bounded functionLinear systemOptimal control Robust optimization Inventory control Viscosity solutionsTrajectoryRobust optimizationSettore MAT/09 - Ricerca OperativaRobust controlOptimal controlMathematics2008 47th IEEE Conference on Decision and Control
researchProduct

Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation

2004

A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the discretization matrices and on an abstract convergence result due to Barles and Souganides.

Nonlinear systemDiscretizationDifferential equationConvergence (routing)Finite differenceCompact finite differenceApplied mathematicsBlack–Scholes modelViscosity solutionHigh-order compact finite differences numerical convergence viscosity solution financial derivativesMathematics
researchProduct

Convergence of dynamic programming principles for the $p$-Laplacian

2018

We provide a unified strategy to show that solutions of dynamic programming principles associated to the $p$-Laplacian converge to the solution of the corresponding Dirichlet problem. Our approach includes all previously known cases for continuous and discrete dynamic programming principles, provides new results, and gives a convergence proof free of probability arguments.

equivalent notions of solutions01 natural sciencesMathematics - Analysis of PDEsnumerical methodsConvergence (routing)FOS: MathematicsApplied mathematicsgeneralized viscosity solutiondiscrete approximationsMathematics - Numerical Analysis0101 mathematicsGeometry and topologyDirichlet problemMathematicsviscosity solutionosittaisdifferentiaaliyhtälötDirichlet problemasymptotic mean value propertiesconvergencenumeeriset menetelmätApplied Mathematics010102 general mathematicsNumerical Analysis (math.NA)dynamic programming principle010101 applied mathematicsDynamic programmingp-Laplacianmonotone approximationsapproksimointiAnalysisAnalysis of PDEs (math.AP)
researchProduct