# American Institute of Mathematical Sciences

September  2018, 8(3&4): 535-555. doi: 10.3934/mcrf.2018022

## Necessary conditions for infinite horizon optimal control problems with state constraints

 1 Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata", Via della Ricerca Scientifica, 1 - 00133 Roma, Italy 2 IMJ-PRG, UMR 7586 CNRS, Sorbonne Université, case 247, 4 place Jussieu, 75252 Paris, France

Received  November 2017 Revised  January 2018 Published  September 2018

Fund Project: The research of third author benefited from the support of the FMJH Program Gaspard Monge in optimization and operation research, and from the support to this program from EDF under the grant PGMO 2015-2832H.

Partial and full sensitivity relations are obtained for nonauto-nomous optimal control problems with infinite horizon subject to state constraints, assuming the associated value function to be locally Lipschitz in the state. Sufficient structural conditions are given to ensure such a Lipschitz regularity in presence of a positive discount factor, as it is typical of macroeconomics models.

Citation: Vincenzo Basco, Piermarco Cannarsa, Hélène Frankowska. Necessary conditions for infinite horizon optimal control problems with state constraints. Mathematical Control & Related Fields, 2018, 8 (3&4) : 535-555. doi: 10.3934/mcrf.2018022
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