Search results for "discrete approximations"

showing 2 items of 2 documents

Controlled polyhedral sweeping processes: existence, stability, and optimality conditions

2021

This paper is mainly devoted to the study of controlled sweeping processes with polyhedral moving sets in Hilbert spaces. Based on a detailed analysis of truncated Hausdorff distances between moving polyhedra, we derive new existence and uniqueness theorems for sweeping trajectories corresponding to various classes of control functions acting in moving sets. Then we establish quantitative stability results, which provide efficient estimates on the sweeping trajectory dependence on controls and initial values. Our final topic, accomplished in finite-dimensional state spaces, is deriving new necessary optimality and suboptimality conditions for sweeping control systems with endpoint constrain…

49M25Applied Mathematics[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Existence of feasible solutions510Sweeping processQualitative stabilityOptimal controlMoving polyhedraOptimization and Control (math.OC)necessary optimality and suboptimality conditionsDiscrete approximationsFOS: MathematicsNecessary optimality and suboptimality conditions 2010 MSC: 49J5249J52 49J53 49K24 49M25[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]49K2449J52Mathematics - Optimization and ControlAnalysis49J53
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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)
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