Dynamic Programming

Abstract

Dynamic programming is an optimization method that transforms a complex problem into a sequence of simpler problems. A sequence of simpler problems can be dealt with a variety of optimization techniques that can be employed to solve particular aspects of a more general formulation. Dynamic programming can be top-down or bottom-up oriented. Three most important characteristics of dynamic programming problems are the following:

• Multiple stages, which are solved sequentially one stage at a time.

• States, which reflect the information required to assess the consequences that the current decision has on future actions.

• Recursive optimization, which builds to a solution of the overall N-stage problem by first solving a one-stage problem and sequentially including one stage at a time and solving one-stage problems until the overall optimum has been found.

No human investigation can be called real science if it cannot be demonstrated mathematically

Leonardo da Vinci