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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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Turnpike Properties in the Calculus of Variations and Optimal Control (Hardcover, 2006 ed.)
Loot Price: R3,117
Discovery Miles 31 170
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Turnpike Properties in the Calculus of Variations and Optimal Control (Hardcover, 2006 ed.)
Series: Nonconvex Optimization and Its Applications, 80
Expected to ship within 10 - 15 working days
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This monograph is devoted to recent progress in the turnpike t-
ory. Turnpike properties are well known in mathematical economics.
The term was ?rst coined by Samuelson who showed that an e?cient
expanding economy would for most of the time be in the vicinity of
a balanced equilibrium path (also called a von Neumann path) [78,
79]. These properties were studied by many authors for optimal
trajec- ries of a Neumann-Gale model determined by a superlinear
set-valued mapping. In the monograph we discuss a number of results
conce- ing turnpike properties in the calculus of variations and
optimal control which were obtained by the author in the last ten
years. These results
showthattheturnpikepropertiesareageneralphenomenonwhichholds for
various classes of variational problems and optimal control
problems. Turnpike properties are studied for optimal control
problems on- nite time intervals [T ,T ] of the real line.
Solutions of such problems 1 2 (trajectories) always depend on the
time interval [T ,T ], an optimality 1 2 criterion which is usually
determined by a cost function, and on data which is some initial
conditions. In the turnpike theory we are int- ested in the
structure of solutions of optimal problems. We study the behavior
of solutions when an optimality criterion is ?xed while T ,T 1 2
andthedatavary.
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