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Convergence of approximate solutions of variational problems

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Języki publikacji
EN
Abstrakty
EN
We study the structure of approximate solutions of autonomous variational problems on large finite intervals. In our previous research, which was summarized in Zaslavski (2006b), we showed that approximate solutions are determined mainly by the integrand, and are essentially independent of the choice of time interval and data, except in regions close to the endpoints of the time interval. In the present paper we establish convergence of approximate solutions in regions close to the endpoints of the time intervals.
Rocznik
Strony
1607--1629
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
Bibliografia
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  • LEIZAROWITZ, A. and MIZEL, V.J. (1989) One dimensional infinite horizon variational problems arising in continuum mechanics. Arch. Rational Mech. Anal. 106, 161-194.
  • 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.
  • MAKAROV, V.L. and RUBINOV, A.M. (1977) Mathematical Theory of Economic Dynamics and Equilibria. Springer-Verlag, New York.
  • MARCUS, M. and ZASLAVSKI, A.J. (1999) The structure of extremals of a class of second order variational problems. Ann. Inst. H. Poincare, Anal. Non Lineaire 16, 593-629.
  • MARCUS, M. and ZASLAVSKI, A.J. (2002) The structure and limiting behavior of locally optimal minimizers. Ann. Inst. H. Poincare, Anal. Non Lineaire 19, 343-370.
  • MORDUKHOVICH, B. (1990) Minimax design for a class of distributed parameter systems. Automat. Remote Control 50, 1333-1340.
  • MORDUKHOVICH, B. and SHVARTSMAN, I. (2004) Optimization and feedback control of constrained parabolic systems under uncertain perturbations. Optimal Control, Stabilization and Nonsmooth Analysis. Lecture Notes Control Inform. Sci. Springer, 121-132.
  • PICKENHAIN, S. and LUKINA, V. (2006) Sufficiency conditions for infinite horizon optimal control problems. Recent Advances in Optimization. Proceedings of the 12th French-German-Spanish Conference on Optimization, Avignon. Springer, 217-232.
  • SAMUELSON, P. A. (1965) A catenary turnpike theorem involving consumption and the golden rule. American Economic Review 55, 486-496.
  • ZASLAVSKI, A.J. (1996) Dynamic properties of optimal solutions of variational problems. Nonlinear Analysis: Theory, Methods and Applications 27, 895-931.
  • ZASLAVSKI, A.J. (1998) Existence and uniform boundedness of optimal solutions of variational problems. Abstract and Applied Analysis 3, 265-292.
  • ZASLAVSKI, A.J. (1999) Turnpike property for extremals of variational problems with vector-valued functions. Transactions of the AMS 351, 211-231.
  • ZASLAVSKI, A.J. (2006a) A nonintersection property for extremals of variational problems with vector-valued functions. Ann. Inst. H. Poincare, Anal, non linéaize 23, 929-948.
  • ZASLAVSKI, A.J. (2006b) Turnpike Properties in the Calculus of Variations and Optimal Control. Springer, New York.
  • ZASLAVSKI, A.J. (2008) Turnpike properties of approximate solutions of autonomous variational problems. Control and Cybernetics 37, 491-512.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0046-0032
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