Structure of approximate solutions of variational problems with extended-valued convex integrands

Alexander J. Zaslavski

ESAIM: Control, Optimisation and Calculus of Variations (2008)

  • Volume: 15, Issue: 4, page 872-894
  • ISSN: 1292-8119

Abstract

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In this work we study the structure of approximate solutions of autonomous variational problems with a lower semicontinuous strictly convex integrand f : Rn×Rn → R1 ∪ { ∞ } , where Rn is the n-dimensional Euclidean space. We obtain a full description of the structure of the approximate solutions which is independent of the length of the interval, for all sufficiently large intervals.

How to cite

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Zaslavski, Alexander J.. "Structure of approximate solutions of variational problems with extended-valued convex integrands." ESAIM: Control, Optimisation and Calculus of Variations 15.4 (2008): 872-894. <http://eudml.org/doc/90942>.

@article{Zaslavski2008,
abstract = { In this work we study the structure of approximate solutions of autonomous variational problems with a lower semicontinuous strictly convex integrand f : Rn×Rn$\to$R1$\cup$$\\{\infty\\}$, where Rn is the n-dimensional Euclidean space. We obtain a full description of the structure of the approximate solutions which is independent of the length of the interval, for all sufficiently large intervals. },
author = {Zaslavski, Alexander J.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Good function; infinite horizon; integrand; overtaking optimal function; turnpike property; approximate solutions; overtaking optimal function},
language = {eng},
month = {8},
number = {4},
pages = {872-894},
publisher = {EDP Sciences},
title = {Structure of approximate solutions of variational problems with extended-valued convex integrands},
url = {http://eudml.org/doc/90942},
volume = {15},
year = {2008},
}

TY - JOUR
AU - Zaslavski, Alexander J.
TI - Structure of approximate solutions of variational problems with extended-valued convex integrands
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2008/8//
PB - EDP Sciences
VL - 15
IS - 4
SP - 872
EP - 894
AB - In this work we study the structure of approximate solutions of autonomous variational problems with a lower semicontinuous strictly convex integrand f : Rn×Rn$\to$R1$\cup$$\{\infty\}$, where Rn is the n-dimensional Euclidean space. We obtain a full description of the structure of the approximate solutions which is independent of the length of the interval, for all sufficiently large intervals.
LA - eng
KW - Good function; infinite horizon; integrand; overtaking optimal function; turnpike property; approximate solutions; overtaking optimal function
UR - http://eudml.org/doc/90942
ER -

References

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  1. H. Atsumi, Neoclassical growth and the efficient program of capital accumulation. Rev. Econ. Studies32 (1965) 127–136.  
  2. L. Cesari, Optimization – theory and applications. Springer-Verlag, New York (1983).  
  3. D. Gale, On optimal development in a multi-sector economy. Rev. Econ. Studies34 (1967) 1–18.  
  4. M. Giaquinta and E. Guisti, On the regularity of the minima of variational integrals. Acta Math.148 (1982) 31–46.  
  5. A. Leizarowitz, Infinite horizon autonomous systems with unbounded cost. Appl. Math. Opt.13 (1985) 19–43.  
  6. A. Leizarowitz and V.J. Mizel, One dimensional infinite horizon variational problems arising in continuum mechanics. Arch. Rational Mech. Anal.106 (1989) 161–194.  
  7. M. Marcus and A.J. Zaslavski, The structure of extremals of a class of second order variational problems. Ann. Inst. H. Poincaré Anal. Non Linéaire16 (1999) 593–629.  
  8. L.W. McKenzie Classical general equilibrium theory. The MIT press, Cambridge, Massachusetts, USA (2002).  
  9. J. Moser, Minimal solutions of variational problems on a torus. Ann. Inst. H. Poincaré Anal. Non Linéaire3 (1986) 229–272.  
  10. P.H. Rabinowitz and E. Stredulinsky, On some results of Moser and of Bangert. Ann. Inst. H. Poincaré Anal. Non Linéaire21 (2004) 673–688.  
  11. P.H. Rabinowitz and E. Stredulinsky, On some results of Moser and of Bangert. II. Adv. Nonlinear Stud.4 (2004) 377–396.  
  12. R.T. Rockafellar, Convex analysis. Princeton University Press, Princeton, USA (1970).  
  13. P.A. Samuelson, A catenary turnpike theorem involving consumption and the golden rule. Am. Econ. Rev.55 (1965) 486–496.  
  14. C.C. von Weizsacker, Existence of optimal programs of accumulation for an infinite horizon. Rev. Econ. Studies32 (1965) 85–104.  
  15. A.J. Zaslavski, Optimal programs on infinite horizon 1. SIAM J. Contr. Opt.33 (1995) 1643–1660.  
  16. A.J. Zaslavski, Optimal programs on infinite horizon 2. SIAM J. Contr. Opt.33 (1995) 1661–1686.  
  17. A.J. Zaslavski, Turnpike properties in the calculus of variations and optimal control. Springer, New York (2006).  
  18. A.J. Zaslavski, Structure of extremals of autonomous convex variational problems. Nonlinear Anal. Real World Appl.8 (2007) 1186–1207.  
  19. A.J. Zaslavski, A turnpike result for a class of problems of the calculus of variations with extended-valued integrands. J. Convex Analysis (to appear).  

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