![]() ![]() Our rule runs faster than comparable rules and discovers shorter, more efficient solution horizons. If no better action can be found, the candidate action is deemed optimal. ![]() Given a candidate policy, the rule uses a mathematical program that searches for other possibly optimal initial actions within the space of feasible truncations. We present such a stopping rule for problems with unbounded rewards. The associated objective value may also be unbounded in this case. This horizon is known as a solution horizon and can be discovered by considering a series of truncations of the problem until a stopping rule guaranteeing initial decision optimality is satisfied. Question: UNBOUNDED SOLUTION In some LP models, the solution space is unbounded in at least one variable-meaning that variables may be increased indefinitely without violating any of the constraints. The optimal initial action can be identified by finding a time horizon so long that data beyond it has no effect on the initial decision. A bounded solution space occurs when the optimal solution of the problem lies within a finite range. Often, only the optimality of the initial action is of importance to the decision-maker: once it has been identified, the procedure can be repeated to generate a plan of arbitrary length. An unbounded solution space occurs when the objective function can be made arbitrarily large or small, and there is no optimal solution. Unfortunately, these problems are notoriously difficult to solve, due to their infinite dimensionality. Infinite-horizon non-stationary Markov decision processes provide a general framework to model many real-life decision-making problems, e.g., planning equipment maintenance. In mathematical optimization, a feasible region, feasible set, search space, or solution space is the set of all possible points of an optimization problem. a) If the feasible polytope described by the solution space of a linear programming problem is unbounded then there is no optimal solution b) If there are two basic optimal feasible solutions then there is an infinity of optimal feasible solutions. ![]()
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