On the Value-Function of an Infinite-Horizon Linear-Quadratic Problem

J. Blot and Philippe Michel

Papiers d'Economie Mathématique et Applications from Université Panthéon-Sorbonne (Paris 1)

Abstract: For a discrete-time infinite-horizon linear-quadratic optimal control problem, under the assumption of the nonemptyness of the set of the asmissible process, we prove the existence and the uniqueness of an optimal process, we prove that the value-function is a quadratic function of the initial state, and we characterize the matrix of this quadratic function among the solutions of an algebraic Raccati equation by using a fixed point theorem.

Keywords: MATHEMATICS (search for similar items in EconPapers)
JEL-codes: C61 C60 (search for similar items in EconPapers)
Date: 2001

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Persistent link: http://EconPapers.repec.org/RePEc:fth:pariem:2001.34

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