zbMATH — the first resource for mathematics

An approximation framework for infinite horizon optimization problems in a mathematical programming setting. (English) Zbl 0971.90101
Nguyen, Van Hien (ed.) et al., Optimization. Proceedings of the 9th Belgian-French-German conference, Namur, Belgium, September 7-11, 1998. Berlin: Springer. Lect. Notes Econ. Math. Syst. 481, 181-202 (2000).
Summary: Dynamic optimization problems, including optimal control problems, have typically relied on the solution techniques of dynamic programming, involving the sequential solution of certain optimality equations. However, many problems cannot be handled this way, due to complex constraints, a continuous state space, and other complicating factors. When recast as mathematical programs relying on the powerful tools of optimization, especially duality, and decomposability to deal with very large problems, the boundaries imposed by dynamic programming are lifted. This paper develops approximation techniques for stationary infinite horizon problems with discounted costs, in the framework of mathematical programming. A reference is given for parallel results for stochastic dynamic optimization problems.
For the entire collection see [Zbl 0935.00054].

90C39 Dynamic programming
90C15 Stochastic programming