underproblem

Underproblem is a term used in problem formulation to denote a problem that is underspecified or underconstrained, lacking sufficient constraints, data, or objectives to determine a unique or stable solution without external assumptions. It stands in contrast to well-posed problems, which specify exact goals and criteria.

In practice, underproblems exhibit multiple admissible solutions, high sensitivity to initial assumptions, and dependence on judgments, priors, or contextual information not included in the problem statement. They are common in early design stages, exploratory research, or interactive systems where users gradually reveal requirements.

Examples include: determining a production plan with the goals of minimizing cost but without fixed capacity or demand; creating a user interface without defined usability criteria; or solving a puzzle that asks for “any solution” without constraints.

Handling underproblems involves eliciting constraints and objectives, performing assumption analysis, and adopting approaches that generate robust or preference-aware solutions, such as scenario analysis, constraint elicitation, multi-criteria decision methods, or convex relaxation with explicit priors.

See also: underconstrained systems, ill-posed problems, problem framing, optimization.