Asymptotical Behavior of Optimal Trajectories and Turnpike Theorems

  • Natali Hritonenko
  • Yuri Yatsenko
Part of the Applied Optimization book series (APOP, volume 4)


This chapter is the continuation of Chapter 4. Here the investigation of the basic optimization problem (OP1) for the simplest one-sector IDM of economic renovation is completed. First, the integral-functional equation for turnpike trajectories is studied in Section 5.1. This equation represents an analog of dual problem for the OP1 and is substantially complicated from the viewpoint of its solvability. The theorems about the existence and asymptotics of its solutions are established. It allows to prove in Section 5.2 the different turnpike theorems (in normal, strong and the strongest forms) for the optimal lifetime of EUs in OP1.


Optimal Trajectory Unique Fixed Point Infinite Interval Optimal Lifetime Quasistationary Solution 
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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Natali Hritonenko
    • 1
  • Yuri Yatsenko
    • 2
  1. 1.Department of CyberneticsKiev UniversityKievUkraine
  2. 2.Glushkov Institute of CyberneticsUkrainian Academy of SciencesKievUkraine

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