The selection problem for discounted Hamilton–Jacobi equations: Some non-convex cases

Diogo A. Gomes, Hiroyoshi Mitake, Hung V. Tran

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

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 languageEnglish (US)
Pages (from-to)345-364
Number of pages20
JournalJournal of the Mathematical Society of Japan
Volume70
Issue number1
DOIs
StatePublished - 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

Fingerprint

Dive into the research topics of 'The selection problem for discounted Hamilton–Jacobi equations: Some non-convex cases'. Together they form a unique fingerprint.

Cite this