This article is about the topic in optimization. For the topic in dynamical systems, see Barrier certificate.
In constrained optimization, a field of mathematics, a barrier function is a continuous function whose value increases to infinity as its argument approaches the boundary of the feasible region of an optimization problem.[1][2] Such functions are used to replace inequality constraints by a penalizing term in the objective function that is easier to handle. A barrier function is also called an interior penalty function, as it is a penalty function that forces the solution to remain within the interior of the feasible region.
The two most common types of barrier functions are inverse barrier functions and logarithmic barrier functions. Resumption of interest in logarithmic barrier functions was motivated by their connection with primal-dual interior point methods.
^Nesterov, Yurii (2018). Lectures on Convex Optimization (2 ed.). Cham, Switzerland: Springer. p. 56. ISBN 978-3-319-91577-7.
^Nocedal, Jorge; Wright, Stephen (2006). Numerical Optimization (2 ed.). New York, NY: Springer. p. 566. ISBN 0-387-30303-0.
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