MMP.8:1 - Problem frame

Use this pattern when a mathematical problem mixes quantities you may choose with quantities you do not control, or when a proposed solution depends on information that arrives too late. A solver can find a configuration for each possible circumstance while leaving you unable to select one in advance. A simulation can show a successful continuation because it chose an environmental value that the acting system cannot choose.

Begin with one proposed action. Ask what will be known when it must be chosen, which quantities remain outside that choice, and what result the action must achieve. Construct two possible circumstances that look the same at that moment. If the proposal assigns different actions to them, it needs another observation, a different decision time or a different policy.

The result is a mathematical formulation of the available choices and the requirement they must satisfy, including their dependence on information. It can establish a feasible fixed choice, a policy, a counterexample to the proposal or the missing contribution. This is a general modeling method for design, prediction and control questions. It develops the formulation before a solver or a control algorithm is selected.

The finite examples need elementary sets, inequalities and the meanings of ‘there exists’ and ‘for every’. More demanding cases can require optimization, stochastic processes or control theory. If the answer condition and available information are already correctly formulated, use C.29.2 or the applicable computational method to obtain the result.