Second-order sensitivity relations and regularity of the value function\n for Mayer's problem in optimal control

2014/08/22 by Piermarco Cannarsa, Cannarsa, Piermarco, Hélène Frankowska +3 · 1 citation
Computer Science · Mathematics · #34A60 #49J53 #Advanced Optimization Algorithms Research #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Nonlinear Partial Differential Equations #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1408.5354

openalex publication_date 2014/08/22 · openalex created_date 2022/12/25 · openalex updated_date 2026/07/28

Abstract

This paper investigates the value function, V, of a Mayer optimal control\nproblem with the state equation given by a differential inclusion. First, we\nobtain an invariance property for the proximal and Fr 'echet subdifferentials\nof V along optimal trajectories. Then, we extend the analysis to the\nsub/superjets of V, obtaining new sensitivity relations of second order. By\napplying sensitivity analysis to exclude the presence of conjugate points, we\ndeduce that the value function is twice differentiable along any optimal\ntrajectory starting at a point at which V is proximally subdifferentiable. We\nalso provide sufficient conditions for the local C² regularity of V on\ntubular neighborhoods of optimal trajectories.\n

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