Existence of solutions for a class of nonconcave infinite horizon optimal control problems

References

• Anderson , BDO and Moore , JB . 1971 . Linear Optimal Control , Englewood Cliffs , NJ : Prentice-Hall .
   Google Scholar
• Aubry , S and Le Daeron , PY . 1983 . The discrete Frenkel-Kontorova model and its extensions I . Physica D , 8 : 381 – 422 .
   Web of Science ®Google Scholar
• Baumeister , J , Leitao , A and Silva , GN . 2007 . On the value function for nonautonomous optimal control problem with infinite horizon . Syst. Control Lett. , 56 : 188 – 196 .
   Web of Science ®Google Scholar
• Blot , J . 2009 . Infinite-horizon Pontryagin principles without invertibility . J. Nonlinear Convex Anal. , 10 : 177 – 189 .
   Web of Science ®Google Scholar
• Blot , J and Cartigny , P . 2000 . Optimality in infinite-horizon variational problems under sign conditions . J. Optim. Theory Appl. , 106 : 411 – 419 .
   Web of Science ®Google Scholar
• Blot , J and Hayek , N . 2000 . Sufficient conditions for infinite-horizon calculus of variations problems . ESAIM Control Optim. Calc. Var. , 5 : 279 – 292 .
   Web of Science ®Google Scholar
• Blot , J and Hayek , N . 2001 . Conjugate points in infinite-horizon control problems . Automat. J. IFAC , 37 : 523 – 526 .
   Web of Science ®Google Scholar
• Cartigny , P and Michel , P . 2003 . On a sufficient transversality condition for infinite horizon optimal control problems . Automat. J. IFAC , 39 : 1007 – 1010 .
   Web of Science ®Google Scholar
• Coleman , BD , Marcus , M and Mizel , VJ . 1992 . On the thermodynamics of periodic phases . Arch. Ration. Mech. Anal. , 117 : 321 – 347 .
   Web of Science ®Google Scholar
• Dechert , WD and Nishimura , K . 1983 . A complete characterization of optimal growth paths in an aggregated model with a nonconcave production function . J. Econom. Theory , 31 : 332 – 354 .
   Web of Science ®Google Scholar
• Gale , D . 1967 . On optimal development in a multi-sector economy . Rev. Econ. Stud. , 34 : 1 – 18 .
   Web of Science ®Google Scholar
• Glizer , V . 2007 . Infinite horizon quadratic control of linear singularly perturbed systems with small state delays: An asymptotic solution of Riccatti-type equation . IMA J. Math. Control Inform. , 24 : 435 – 459 .
   Web of Science ®Google Scholar
• Jasso-Fuentes , H and Hernandez-Lerma , O . 2008 . Characterizations of overtaking optimality for controlled diffusion processes . Appl. Math. Optim. , 57 : 349 – 369 .
   Web of Science ®Google Scholar
• Leizarowitz , A . 1985 . Infinite horizon autonomous systems with unbounded cost . Appl. Math. Optim. , 13 : 19 – 43 .
   Web of Science ®Google Scholar
• Leizarowitz , A . 1986 . Tracking nonperiodic trajectories with the overtaking criterion . Appl. Math. Optim. , 14 : 155 – 171 .
   Web of Science ®Google Scholar
• Leizarowitz , A and Mizel , VJ . 1989 . One dimensional infinite horizon variational problems arising in continuum mechanics . Arch. Ration. Mech. Anal. , 106 : 161 – 194 .
   Web of Science ®Google Scholar
• Leizarowitz , A and Zaslavski , AJ . 2005 . On a class of infinite horizon optimal control problems with periodic cost functions . J. Nonlinear Convex Anal. , 6 : 71 – 91 .
   Web of Science ®Google Scholar
• Lykina , V , Pickenhain , S and Wagner , M . 2008 . Different interpretations of the improper integral objective in an infinite horizon control problem . J. Math. Anal. Appl. , 340 : 498 – 510 .
   Web of Science ®Google Scholar
• Majumdar , M and Mitra , T . 1982 . Intertemporal allocation with a nonconvex technology: The aggregative framework . J. Econ. Theory , 27 : 101 – 136 .
   Web of Science ®Google Scholar
• Makarov , VL and Rubinov , AM . 1977 . Mathematical Theory of Economic Dynamics and Equilibria , New York : Springer-Verlag .
   Google Scholar
• Marcus , M and Zaslavski , AJ . 1999 . The structure of Extremals of a Class of Second Order Variational Problems . Ann. Inst. H. Poincare Anal. Non Lineare , 16 : 593 – 629 .
   Web of Science ®Google Scholar
• McKenzie , LW . 2002 . Classical General Equilibrium Theory , Cambridge , MA : The MIT press .
   Google Scholar
• Mitra , T and Ray , D . 1984 . Dynamic optimization on a nonconvex feasible set: Some general results for nonsmooth technologies . Z. Nationalokonomie , 44 : 151 – 175 .
   Web of Science ®Google Scholar
• Mordukhovich , B . 1990 . Minimax design for a class of distributed parameter systems . Automat. Remote Control , 50 : 1333 – 1340 .
   Web of Science ®Google Scholar
• Mordukhovich , B and Shvartsman , I . 2004 . “ Optimization and Feedback Control of Constrained Parabolic Systems under Uncertain Perturbations ” . In Optimal Control, Stabilization and Nonsmooth Analysis, Lecture Notes in Control and Information Science , 121 – 132 . New York : Springer .
   Google Scholar
• Moser , J . 1986 . Minimal solutions of variational problems on a torus . Ann. Inst. H. Poincare Anal. Non Lineare , 3 : 229 – 272 .
   Web of Science ®Google Scholar
• Pickenhain , S and Lykina , V . 2006 . Sufficiency Conditions for Infinite Horizon Optimal Control Problems, Recent Advances in Optimization, Proceedings of the 12th French-German-Spanish Conference on Optimization , 217 – 232 . Avignon : Springer .
   Google Scholar
• Pickenhain , S , Lykina , V and Wagner , M . 2008 . On the lower semicontinuity of functionals involving Lebesgue or improper Riemann integrals in infinite horizon optimal control problems . Control Cybernet. , 37 : 451 – 468 .
   Web of Science ®Google Scholar
• Prieto-Rumeau , T and Hernandez-Lerma , O . 2005 . Bias and overtaking equilibria for zero-sum continuous-time Markov games . Math. Methods Oper. Res. , 61 : 437 – 454 .
   Web of Science ®Google Scholar
• Samuelson , PA . 1965 . A catenary turnpike theorem involving consumption and the golden rule . Am. Econ. Rev. , 55 : 486 – 496 .
   Web of Science ®Google Scholar
• Skiba , AK . 1978 . Optimal growth with a convex-concave production function . Econometrica , 46 : 527 – 539 .
   Web of Science ®Google Scholar
• von Weizsacker , CC . 1965 . Existence of optimal programs of accumulation for an infinite horizon . Rev. Econ. Stud. , 32 : 85 – 104 .
   Web of Science ®Google Scholar
• Zaslavski , AJ . 1987 . Ground states in Frenkel-Kontorova model . Math. USSR Izv. , 29 : 323 – 354 .
   Google Scholar
• Zaslavski , AJ . 2006 . Turnpike Properties in the Calculus of Variations and Optimal Control , New York : Springer .
   Google Scholar
• Zaslavski , AJ . 2007 . Turnpike results for a discrete-time optimal control system arising in economic dynamics . Nonlinear Anal. , 67 : 2024 – 2049 .
   Web of Science ®Google Scholar
• Zaslavski , AJ . 2009 . Two turnpike results for a discrete-time optimal control systems . Nonlinear Anal. , 71 : 902 – 909 .
   Web of Science ®Google Scholar
• Zaslavski , AJ . 2010 . Optimal solutions for a class of infinite horizon variational problems with extended-valued integrands . Optimization , 59 : 181 – 197 .
   Web of Science ®Google Scholar