In this work we study the structure of approximate solutions of autonomous variational problems with a lower semicontinuous strictly convex integrand : , where is the -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.
Classification : 49J99
Mots clés : good function, infinite horizon, integrand, overtaking optimal function, turnpike property
@article{COCV_2009__15_4_872_0,
author = {Zaslavski, Alexander J.},
title = {Structure of approximate solutions of variational problems with extended-valued convex integrands},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {872--894},
publisher = {EDP-Sciences},
volume = {15},
number = {4},
year = {2009},
doi = {10.1051/cocv:2008053},
zbl = {1175.49002},
mrnumber = {2567250},
language = {en},
url = {www.numdam.org/item/COCV_2009__15_4_872_0/}
}
Zaslavski, Alexander J. Structure of approximate solutions of variational problems with extended-valued convex integrands. ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 4, pp. 872-894. doi : 10.1051/cocv:2008053. http://www.numdam.org/item/COCV_2009__15_4_872_0/
[1] , Neoclassical growth and the efficient program of capital accumulation. Rev. Econ. Studies 32 (1965) 127-136.
[2] , Optimization - theory and applications. Springer-Verlag, New York (1983). | MR 688142 | Zbl 0506.49001
[3] , On optimal development in a multi-sector economy. Rev. Econ. Studies 34 (1967) 1-18.
[4] and , On the regularity of the minima of variational integrals. Acta Math. 148 (1982) 31-46. | MR 666107 | Zbl 0494.49031
[5] , Infinite horizon autonomous systems with unbounded cost. Appl. Math. Opt. 13 (1985) 19-43. | MR 778419 | Zbl 0591.93039
[6] and , One dimensional infinite horizon variational problems arising in continuum mechanics. Arch. Rational Mech. Anal. 106 (1989) 161-194. | MR 980757 | Zbl 0672.73010
[7] and , The structure of extremals of a class of second order variational problems. Ann. Inst. H. Poincaré Anal. Non Linéaire 16 (1999) 593-629. | Numdam | MR 1712568 | Zbl 0989.49003
[8] Classical general equilibrium theory. The MIT press, Cambridge, Massachusetts, USA (2002). | MR 1933283 | Zbl 1020.91002
[9] , Minimal solutions of variational problems on a torus. Ann. Inst. H. Poincaré Anal. Non Linéaire 3 (1986) 229-272. | Numdam | MR 847308 | Zbl 0609.49029
[10] and , On some results of Moser and of Bangert. Ann. Inst. H. Poincaré Anal. Non Linéaire 21 (2004) 673-688. | Numdam | MR 2086754 | Zbl 1149.35341
[11] and , On some results of Moser and of Bangert. II. Adv. Nonlinear Stud. 4 (2004) 377-396. | MR 2100904 | Zbl pre02149270
[12] , Convex analysis. Princeton University Press, Princeton, USA (1970). | MR 274683 | Zbl 0193.18401
[13] , A catenary turnpike theorem involving consumption and the golden rule. Am. Econ. Rev. 55 (1965) 486-496.
[14] , Existence of optimal programs of accumulation for an infinite horizon. Rev. Econ. Studies 32 (1965) 85-104.
[15] , Optimal programs on infinite horizon 1. SIAM J. Contr. Opt. 33 (1995) 1643-1660. | MR 1358089 | Zbl 0847.49021
[16] , Optimal programs on infinite horizon 2. SIAM J. Contr. Opt. 33 (1995) 1661-1686. | MR 1358089 | Zbl 0847.49022
[17] , Turnpike properties in the calculus of variations and optimal control. Springer, New York (2006). | MR 2164615 | Zbl 1100.49003
[18] , Structure of extremals of autonomous convex variational problems. Nonlinear Anal. Real World Appl. 8 (2007) 1186-1207. | MR 2331434 | Zbl pre05168866
[19] , A turnpike result for a class of problems of the calculus of variations with extended-valued integrands. J. Convex Analysis (to appear). | Zbl 1162.49017
