## Abstract

We devise an algorithm for solving the infinite-dimensional linear programs that arise from general deterministic semi-Markov decision processes on Borel spaces. The algorithm constructs a sequence of approximate primal-dual solutions that converge to an optimal one. The innovative idea is to approximate the dual solution with continuous piecewise linear ridge functions that naturally represent functions defined on a high-dimensional domain as linear combinations of functions defined on only a single dimension. This approximation gives rise to a primal/dual pair of semi-infinite programs, for which we show strong duality. In addition, we prove various properties of the underlying ridge functions.

Original language | English (US) |
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Pages (from-to) | 528-550 |

Number of pages | 23 |

Journal | Mathematics of Operations Research |

Volume | 32 |

Issue number | 3 |

DOIs | |

State | Published - Aug 1 2007 |

## Keywords

- Approximate dynamic programming
- Deterministic semi-Markov decision processes
- Infinite/semi-infinite linear programming algorithms
- Ridge function approximations

## ASJC Scopus subject areas

- Mathematics(all)
- Computer Science Applications
- Management Science and Operations Research