Barjäärfunktsioon

Barjäärfunktsioon, also known as a barrier function, is a concept used in optimization and control theory. It is a mathematical function that is added to an objective function to penalize infeasible solutions or to guide a search algorithm towards a feasible region. Typically, a barrier function has a large, positive value as a solution approaches the boundary of the feasible region, effectively making these solutions undesirable. As a solution moves further into the feasible region, the barrier function's value decreases, often approaching zero.

In practice, barrier functions are employed in various optimization algorithms, such as interior-point methods. These methods start from an interior point of the feasible region and iteratively move towards an optimal solution while staying within the bounds. The barrier function ensures that the algorithm never crosses the boundary of the feasible set. The specific form of the barrier function depends on the nature of the constraints. Common examples include the logarithmic barrier function and the inverse barrier function. Their primary purpose is to maintain feasibility throughout the optimization process, preventing the algorithm from diverging or encountering invalid states.