Asymptotical stability of optimal paths in nonconvex problems

Musa A. Mamedov ()
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Musa A. Mamedov: University of Ballarat

Chapter Chapter 5 in Optimization, 2009, pp 95-134 from Springer

Abstract: Abstract In this chapter we study the turnpike property for the nonconvex optimal control problems described by the differential inclusion $$\dot{x} \in a(x)$$ . We study the infinite horizon problem of maximizing the functional $$\int_{0}^{T} u(x(t))\,dt$$ as T grows to infinity. The purpose of this chapter is to avoid the convexity conditions usually assumed in turnpike theory. A turnpike theorem is proved in which the main conditions are imposed on the mapping a and the function u. It is shown that these conditions may hold for mappings a with nonconvex images and for nonconcave functions u.

Keywords: Turnpike property; differential inclusion; functional (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/978-0-387-98096-6_5

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