Abstract
Here, we study the selection problem for the vanishing discount approximation of non-convex, first-order Hamilton–Jacobi equations. While the selection problem is well understood for convex Hamiltonians, the selection problem for non-convex Hamiltonians has thus far not been studied. We begin our study by examining a generalized discounted Hamilton–Jacobi equation. Next, using an exponential transformation, we apply our methods to strictly quasi-convex and to some non-convex Hamilton–Jacobi equations. Finally, we examine a non-convex Hamiltonian with flat parts to which our results do not directly apply. In this case, we establish the convergence by a direct approach.
Original language | English (US) |
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Pages (from-to) | 345-364 |
Number of pages | 20 |
Journal | Journal of the Mathematical Society of Japan |
Volume | 70 |
Issue number | 1 |
DOIs | |
State | Published - 2018 |
Bibliographical note
Publisher Copyright:© 2018 The Mathematical Society of Japan.
Keywords
- Discounted approximation
- Ergodic problems
- Nonlinear adjoint methods
- nonconvex Hamilton–Jacobi equations
ASJC Scopus subject areas
- General Mathematics