barrierfunksjon

Barrierfunksjon, also known as a barrier method or interior-point method in optimization, is a class of algorithms used to solve constrained optimization problems. These methods work by transforming a constrained problem into a sequence of unconstrained problems. This transformation is achieved by adding a penalty term to the objective function, which becomes infinitely large as the solution approaches the boundary of the feasible region.

The core idea behind barrier functions is to stay strictly within the feasible region during the optimization process. As the optimization algorithm iteratively moves towards the solution, the barrier function penalizes the objective function more and more heavily for getting close to the boundary. This effectively "pushes" the solution away from the constraints, ensuring that all intermediate solutions are valid.

Different types of barrier functions exist, such as the logarithmic barrier function and the inverse barrier function. The choice of barrier function can affect the convergence properties and numerical stability of the algorithm. Barrier methods are particularly effective for problems with convex objective functions and convex feasible regions. They have found applications in various fields, including linear programming, quadratic programming, and nonlinear programming, offering a robust approach to handling inequality constraints.