Necessity of limiting co-state arcs in Bolza-type infinite horizon problem

References

• Pontryagin LS, Boltyanskij VG, Gamkrelidze RV, Mishchenko EF. The mathematical theory of optimal processes. Moscow: Fizmatgiz; 1961.
   Google Scholar
• Halkin H. Necessary conditions for optimal control problems with infinite horizons. Econometrica. 1974;42:267–272.
   Web of Science ®Google Scholar
• Kamihigashi T. Necessity of transversality conditions for infinite horizon problems. Econometrica. 2001;69:995–1012.
   Web of Science ®Google Scholar
• Michel P. On the transversality condition in infinite horizon optimal problems. Econometrica. 1982;50:975–984.
   Web of Science ®Google Scholar
• Seierstad A, Sydsæter K. Optimal control theory with economic applications. Amsterdam: North-Holland; 1987.
   Google Scholar
• Smirnov GV. Transversality condition for infinite-horizon problems. J. Optim. Theory Appl. 1996;88:671–688.
   Web of Science ®Google Scholar
• Carlson DA, Haurie AB, Leizarowitz A. Infinite horizon optimal control. Deterministic and stochastic systems. Berlin: Springer; 1991.
   Google Scholar
• Shell K. Applications of Pontryagin’s maximum principle to economics. In: Mathematical systems theory and economics, VII. Berlin: Springer; 1969. p. 241–292.
   Google Scholar
• Aseev SM, Kryazhimskii AV. The Pontryagin maximum principle and problems of optimal economic growth. Proc. Steklov Inst. Math. 2007;257:1–255.
   Google Scholar
• Seierstad A. Necessary conditions for nonsmooth, infinite-horizon optimal control problems. J. Optim. Theory Appl. 1999;103:201–230.
   Web of Science ®Google Scholar
• Aubin J-P, Clarke FH. Shadow prices and duality for a class of optimal control problems. SIAM J. Control Optim. 1979;17:567–586.
   Web of Science ®Google Scholar
• Aseev SM, Kryazhimskii AV. The Pontryagin maximum principle and transversality conditions for a class of optimal control problems with infinite time horizons. SIAM J. Control Optim. 2004;43:1094–1119.
   Google Scholar
• Aseev SM, Kryazhimskii AV, Besov KO. Infinite-horizon optimal control problems in economics. Russ. Math. Surv. 2012;67:195–253.
   Web of Science ®Google Scholar
• Aseev SM, Veliov VM. Maximum principle for infinite-horizon optimal control; problems with dominating discount. Dyn. Cont. Discrete Impulsive Syst. Ser. B. 2012;19:43–63.
   Google Scholar
• Aseev SM, Veliov VM. Needle variations in infinite-horizon optimal control. In: Wolansky G, Zaslavski AJ, editors. Variational and optimal control problems on unbounded domains. Providence (RI): AMS; 2014. p. 1–17. (Contemporary Mathematics; vol. 619).
   Google Scholar
• Khlopin DV. Necessity of vanishing shadow price in infinite horizon control problems. J. Dyn. & Con.Sys. 2013;19, 4:519–552.
   Web of Science ®Google Scholar
• Hammond PJ, Kennan J. Uniformly optimal infinite-horizon plans. Int. Econ. Rev. 1979;20:283–296.
   Web of Science ®Google Scholar
• Balder EJ. An existence result for optimal economic growth problems. J. Math. Anal. 1983;95:195–213.
   Web of Science ®Google Scholar
• Baum RF. Existence theorems for Lagrange control problems with unbounded time domain. J. Optim. Theory Appl. 1976;19:89–116.
   Web of Science ®Google Scholar
• Dmitruk AV, Kuz’kina NV. An existence theorem in an optimal control problem on an infinite time interval. Math. Notes. 2005;78:466–480.
   Web of Science ®Google Scholar
• Khan MA, Zaslavski AJ. On locally optimal programs in the Robinson–Solow–Srinivasan model. J. Econ. 2010;99:65–92.
   Web of Science ®Google Scholar
• Zaslavski AJ. Turnpike properties in the calculus of variations and optimal control. New York (NY): Springer; 2006.
   Google Scholar
• Khlopin DV. On necessary boundary conditions for strongly optimal control in infinite horizon control problems. Bull. Udmurt Univ. Math. Mech. Comput. Sci. 2013;1:49–58. Russian.
   Google Scholar
• Khlopin DV. Necessary conditions of overtaking equilibrium for infinite horizon Mat. Teor. Igr Prilozh. 2013;2:105–136. Russian.
   Google Scholar
• Tolstonogov AA. Differential inclusions in a Banach space. Dordrecht: Kluwer Academic Publishers; 2000.
   Google Scholar
• Bogusz D. On the existence of a classical optimal solution and of an almost strongly optimal solution for an infinite-horizon control problem. J. Optim. Theory Appl. 2013;156:650–682.
   Web of Science ®Google Scholar
• Carlson DA. Uniformly overtaking and weakly overtaking optimal solutions in infinite-horizon optimal control: when optimal solutions are agreeable. J. Optim. Theory Appl. 1990;64:55–69.
   Web of Science ®Google Scholar
• Stern LE. Criteria of optimality in the infinite-time optimal control problem. J. Optim. Theory Appl. 1984;44:497–508.
   Web of Science ®Google Scholar
• Brock WA, Haurie A. On existence of overtaking optimal trajectories over an infinite time horizon. Math. Oper. Res. 1976;1:337–346.
   Google Scholar
• Tan H, Rugh WJ. Nonlinear overtaking optimal control: sufficiency, stability, and approximation. IEEE Trans. Automatic Control. 1998;43:1703–1718.
   Web of Science ®Google Scholar
• Clarke FH. Necessary conditions in dynamic optimization. Providence (RI):AMS; 2005. (Mem. AMS; vol. 816).
   Google Scholar
• Vinter RB. Optimal control. Boston (MA): Birkhäuser; 2000.
   Google Scholar
• Clarke FH. Optimization and nonsmooth analysis. New York (NY): Wiley; 1983.
   Google Scholar
• Seierstad A. Fields of extremals and infinite horizon optimal control problems. Optim. Control Appl. Meth. 1998;19:377–392.
   Web of Science ®Google Scholar
• Sagara N. Value functions and transversality conditions for infinite-horizon optimal control problems. Set-Valued Var. Anal. 2010;18:1–28.
   Web of Science ®Google Scholar
• Koopmans TC. Concepts of optimality and their uses. Nobel Lectures 1975; reproduced in. Amer. Econ. Rev. 1975;1977:261–274.
   Google Scholar
• Aubin J-P, Ekeland I. Applied nonlinear analysis. New York (NY): Wiley; 1984.
   Google Scholar
• Borwein JM, Zhu QJ. Techniques of variational analysis. Berlin: Springer; 2005.
   Google Scholar
• Wagner DH. Survey of measurable selection theorems: an update. In: Közlov D, editor. Measure theory. Vol. 794, Lecture notes in mathematics. Berlin: Springer; 1980. p. 176–219
   Google Scholar