1. Linear programming solutions of periodic optimization problems: approximation of the optimal control
- Author
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Luke Finlay, Vladimir Gaitsgory, Ivan Lebedev, Finlay, Luke, Gaitsgory, Vladimir, and Lebedev, Ivan
- Subjects
Mathematical optimization ,Control and Optimization ,occupational measures ,L-reduction ,linear programming approach ,Applied Mathematics ,Strategy and Management ,Robust optimization ,Approximation algorithm ,Optimal control ,Atomic and Molecular Physics, and Optics ,Stochastic programming ,Linear-fractional programming ,optimal control ,numerical solutions ,Criss-cross algorithm ,Business and International Management ,Electrical and Electronic Engineering ,Randomized rounding ,periodic optimisation ,Mathematics - Abstract
Deterministic long run average problems of optimal control are ''asymptotically equivalent" to infinite-dimensional linear programming problems ( LPP ) and the latter are approximated by finite dimensional LPP. The solutions of this finite dimensional LPP can be used for numerical analysis of periodic optimization problems. In the present paper we establish the convergence of controls constructed on the basis of the solution of the finite dimensional LPP to the optimal control of a periodic optimization problem. Results are illustrated with a numerical example.
- Published
- 2007
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