Necessary Optimality Conditions for Higher-Order Infinite Horizon Variational Problems on Time Scales
- 270 Downloads
We obtain Euler–Lagrange and transversality optimality conditions for higher-order infinite horizon variational problems on a time scale. The new necessary optimality conditions improve the classical results both in the continuous and discrete settings: Our results seem new and interesting even in the particular cases when the time scale is the set of real numbers or the set of integers.
KeywordsTime scales Calculus of variations Infinite horizon problems Euler–Lagrange equations Transversality conditions
This work was supported by FEDER funds through COMPETE—Operational Programme Factors of Competitiveness (“Programa Operacional Factores de Competitividade”) and by Portuguese funds through the Center for Research and Development in Mathematics and Applications (University of Aveiro) and the Portuguese Foundation for Science and Technology (“FCT—Fundação para a Ciência e a Tecnologia”), within project PEst-C/MAT/UI4106/2011 with COMPETE number FCOMP-01-0124-FEDER-022690. Torres was also supported by project PTDC/MAT/113470/2009.
- 1.Chiang, A.C.: Elements of Dynamic Optimization. McGraw-Hill, Singapore (1992) Google Scholar
- 14.Mordukhovich, B.S.: Variational Analysis and Generalized Differentiation II. Grundlehren der Mathematischen Wissenschaften, vol. 331. Springer, Berlin (2006) Google Scholar
- 18.Cai, D., Nitta, T.G.: Transversality conditions for higher order infinite horizon discrete time optimization problems (2010). arXiv:1004.3093 [math.OC]
- 23.Lang, S.: Undergraduate Analysis. Springer, New York (1997) Google Scholar