Abstract
AbstractWe show a connection between global unconstrained optimization of a continuous function f and weak KAM theory for an eikonal-type equation arising also in ergodic control. A solution v of the critical Hamilton–Jacobi equation is built by a small discount approximation as well as the long time limit of an associated evolutive equation. Then v is represented as the value function of a control problem with target, whose optimal trajectories are driven by a differential inclusion describing the gradient descent of v. Such trajectories are proved to converge to the set of minima of f, using tools in control theory and occupational measures. We prove also that in some cases the set of minima is reached in finite time.
Funder
Università degli Studi di Padova
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Control and Optimization
Reference34 articles.
1. Alvarez, O., Bardi, M.: Ergodicity, Stabilization, and Singular Perturbations for Bellman–Isaacs Equations. American Mathematical Society, Providence (2010)
2. Arisawa, M., Lions, P.-L.: On ergodic stochastic control. Commun. Part. Differ. Equ. 23, 2187–2217 (1998)
3. Artstein, Z., Gaitsgory, V.: The value function of singularly perturbed control systems. Appl. Math. Optim. 41, 425–445 (2000)
4. Bardi, M., Capuzzo-Dolcetta, I.: Optimal Control and Viscosity Solutions of Hamilton–Jacobi–Bellman Equations. Springer, Berlin (2008)
5. Barles, G., Roquejoffre, J.-M.: Ergodic type problems and large time behaviour of unbounded solutions of Hamilton–Jacobi equations. Commun. Part. Differ. Equ. 31, 1209–1225 (2006)
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