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

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

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

## Access Full Article

top## Abstract

top## How to cite

topZaslavski, 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

top- H. Atsumi, Neoclassical growth and the efficient program of capital accumulation. Rev. Econ. Studies32 (1965) 127–136.
- L. Cesari, Optimization – theory and applications. Springer-Verlag, New York (1983). Zbl0506.49001
- D. Gale, On optimal development in a multi-sector economy. Rev. Econ. Studies34 (1967) 1–18.
- M. Giaquinta and E. Guisti, On the regularity of the minima of variational integrals. Acta Math.148 (1982) 31–46. Zbl0494.49031
- A. Leizarowitz, Infinite horizon autonomous systems with unbounded cost. Appl. Math. Opt.13 (1985) 19–43. Zbl0591.93039
- A. Leizarowitz and V.J. Mizel, One dimensional infinite horizon variational problems arising in continuum mechanics. Arch. Rational Mech. Anal.106 (1989) 161–194. Zbl0672.73010
- 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. Zbl0989.49003
- L.W. McKenzie Classical general equilibrium theory. The MIT press, Cambridge, Massachusetts, USA (2002).
- J. Moser, Minimal solutions of variational problems on a torus. Ann. Inst. H. Poincaré Anal. Non Linéaire3 (1986) 229–272. Zbl0609.49029
- P.H. Rabinowitz and E. Stredulinsky, On some results of Moser and of Bangert. Ann. Inst. H. Poincaré Anal. Non Linéaire21 (2004) 673–688. Zbl1149.35341
- P.H. Rabinowitz and E. Stredulinsky, On some results of Moser and of Bangert. II. Adv. Nonlinear Stud.4 (2004) 377–396. Zbl1229.35047
- R.T. Rockafellar, Convex analysis. Princeton University Press, Princeton, USA (1970). Zbl0193.18401
- P.A. Samuelson, A catenary turnpike theorem involving consumption and the golden rule. Am. Econ. Rev.55 (1965) 486–496.
- C.C. von Weizsacker, Existence of optimal programs of accumulation for an infinite horizon. Rev. Econ. Studies32 (1965) 85–104.
- A.J. Zaslavski, Optimal programs on infinite horizon 1. SIAM J. Contr. Opt.33 (1995) 1643–1660. Zbl0847.49021
- A.J. Zaslavski, Optimal programs on infinite horizon 2. SIAM J. Contr. Opt.33 (1995) 1661–1686. Zbl0847.49022
- A.J. Zaslavski, Turnpike properties in the calculus of variations and optimal control. Springer, New York (2006). Zbl1100.49003
- A.J. Zaslavski, Structure of extremals of autonomous convex variational problems. Nonlinear Anal. Real World Appl.8 (2007) 1186–1207. Zbl1186.49008
- 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). Zbl1162.49017

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.