Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-19T17:54:21.221Z Has data issue: false hasContentIssue false
  • English
  • Français

Structure of approximate solutions of variational problemswith extended-valued convexintegrands

Published online by Cambridge University Press:  20 August 2008

Alexander J. Zaslavski
Alexander J. Zaslavski*
Affiliation:
Department of Mathematics, The Technion-Israel Institute of Technology, 32000 Haifa, Israel. [email protected]
Get access

Abstract

In this work we study the structure of approximatesolutions of autonomous variational problems with a lowersemicontinuous strictly convex integrand f : Rn ×Rn $\to$ R 1 $\cup$ $\{\infty\}$ , where Rn is the n-dimensional Euclideanspace. We obtain a full description of the structure of theapproximate solutions which is independent of the length of theinterval, for all sufficiently large intervals.

Keywords

Good functioninfinite horizonintegrandovertakingoptimal functionturnpike property
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 15 , Issue 4 , October 2009 , pp. 872 - 894
Copyright
© EDP Sciences, SMAI, 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Atsumi, H., Neoclassical growth and the efficient program of capital accumulation. Rev. Econ. Studies 32 (1965) 127–136. CrossRef
L. Cesari, Optimization – theory and applications. Springer-Verlag, New York (1983).
On, D. Gale optimal development in a multi-sector economy. Rev. Econ. Studies 34 (1967) 1–18.
Giaquinta, M. and Guisti, E., On the regularity of the minima of variational integrals. Acta Math. 148 (1982) 31–46. CrossRef
Leizarowitz, A., Infinite horizon autonomous systems with unbounded cost. Appl. Math. Opt. 13 (1985) 19–43. CrossRef
Leizarowitz, A. and Mizel, V.J., One dimensional infinite horizon variational problems arising in continuum mechanics. Arch. Rational Mech. Anal. 106 (1989) 161–194. CrossRef
Marcus, M. and Zaslavski, A.J., The structure of extremals of a class of second order variational problems. Ann. Inst. H. Poincaré Anal. Non Linéaire 16 (1999) 593–629. CrossRef
L.W. McKenzie Classical general equilibrium theory. The MIT press, Cambridge, Massachusetts, USA (2002).
Moser, J., Minimal solutions of variational problems on a torus. Ann. Inst. H. Poincaré Anal. Non Linéaire 3 (1986) 229–272. CrossRef
Rabinowitz, P.H. and Stredulinsky, E., On some results of Moser and of Bangert. Ann. Inst. H. Poincaré Anal. Non Linéaire 21 (2004) 673–688. CrossRef
Rabinowitz, P.H. and Stredulinsky, E., On some results of Moser and of Bangert. II. Adv. Nonlinear Stud. 4 (2004) 377–396. CrossRef
R.T. Rockafellar, Convex analysis. Princeton University Press, Princeton, USA (1970).
Samuelson, P.A., A catenary turnpike theorem involving consumption and the golden rule. Am. Econ. Rev. 55 (1965) 486–496.
von Weizsacker, C.C., Existence of optimal programs of accumulation for an infinite horizon. Rev. Econ. Studies 32 (1965) 85–104. CrossRef
Zaslavski, A.J., Optimal programs on infinite horizon 1. SIAM J. Contr. Opt. 33 (1995) 1643–1660. CrossRef
Zaslavski, A.J., Optimal programs on infinite horizon 2. SIAM J. Contr. Opt. 33 (1995) 1661–1686. CrossRef
A.J. Zaslavski, Turnpike properties in the calculus of variations and optimal control. Springer, New York (2006).
Zaslavski, A.J., Structure of extremals of autonomous convex variational problems. Nonlinear Anal. Real World Appl. 8 (2007) 1186–1207. CrossRef
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).