Nonoptimal

Nonoptimal is an adjective used to describe outcomes, decisions, or solutions that are not the best possible within a given model or set of constraints. In optimization and related fields, the opposite of optimal is optimal; a nonoptimal solution fails to achieve the global optimum and may be suboptimal in the sense of being local or simply inferior to the best feasible result.

Nonoptimality can arise from many sources: incomplete search or early termination in iterative methods, the use of simplifying approximations or heuristics, noisy or mis-specified data, discretization, or numerical errors. In decision problems, time or resource constraints may force choosing a nonoptimal option.

Examples include: in linear programming, a feasible solution that does not minimize the objective function is nonoptimal. In combinatorial optimization, heuristics for problems like the traveling salesman often yield nonoptimal tours. In machine learning, models trained with limited data or iterations may be nonoptimal compared with fully converged models.

Measuring nonoptimality often involves the optimality gap, regret, or comparison to a known optimum. Theoretical optimality conditions, such as the Karush-Kuhn-Tucker conditions, identify when a solution is optimal; violation implies nonoptimality. Algorithms may provide bounds on how far a produced solution is from optimal, known as approximation ratios or suboptimality guarantees.

See also: optimality, optimal solution, suboptimal, approximation algorithm, duality, relaxation, heuristic, convergence.