Dynamic programming using local optimality conditions for action elimination

In the theory of dynamic programming (DP) the elimination of non-optimal actions is an important topic. For many DP problems the calculation is slow and action elimination helps to speed up the calculation. A great part of this thesis is dedicated to the development of action elimination procedures for various classes of DP problems. Common to all these action elimination procedures is that they are based on local optimality conditions. Among the classes of DP problems looked at are deterministic allocation problems and stochastic problems with either continuous or discrete state and action spaces. For DP problems with continuous state and action space the action elimination procedures are based on the Fritz-John first order optimality conditions. For problems with discrete state and action space the action elimination procedures are based on local optimality conditions for discrete problems. It is shown that action elimination based on local optimality conditions usually leads to a speed-up of one order of magnitude. Chapters 7 and 8 discuss a constrained non-linear oil production optimization problem. In this problem most functions involved are continuous but a few functions contain discontinuities, which seriously undermines the scope of local optimization. A hybrid algorithm combining a dual method, DP and local optimization is proposed and computational results are presented. These results are then compared to those of another hybrid algorithm, which combines Tabu Search and local optimization.