Mitteoptimaalseid

Mitteoptimaalseid is Estonian for non-optimal or not optimal, and is used in optimization to describe solutions that do not achieve the best possible value of an objective function under given constraints. The term is often employed to distinguish feasible solutions that fail to reach the global optimum from those that are optimal.

In a typical optimization problem, one seeks to minimize or maximize an objective function f(x) subject to constraints. A feasible solution x* is non-optimal if there exists another feasible solution y such that f(y) is better than f(x*), according to the objective (for minimization, f(y) < f(x*); for maximization, f(y) > f(x*)). Non-optimal solutions can be globally non-optimal, or they can be locally non-optimal in the sense that no nearby point improves the value even though better solutions exist elsewhere.

Non-optimal solutions commonly arise in practice because many algorithms only explore parts of the search space or terminate before reaching the global optimum. They are also common in heuristic or approximate methods, where computational limits or imperfect models lead to feasible solutions that are not optimal.

Identifying non-optimality involves verifying optimality conditions or computing bounds. Certificates of suboptimality, such as a duality gap in certain problems or violation of necessary optimality conditions (like the Karush-Kuhn-Tucker conditions in constrained optimization), can confirm that a solution is not optimal. In multi-objective contexts, non-optimal solutions may still be acceptable if they offer good trade-offs among competing goals.

See also: optimization, optimal solution, local optimum, global optimum, duality, KKT conditions, feasibility, objective function.