Barrier function

<p>In constrained <a href="/facts/Mathematical_optimization/oRn8Iv5I">optimization</a>, a field of <a href="/facts/Mathematics/pxTouaz4">mathematics</a>,  a barrier function is a <a href="/facts/Continuous_function/sKbl02pB">continuous function</a> whose value increases to infinity as its argument approaches the boundary of the <a href="/facts/Candidate_solution/cJUKNCmM">feasible region</a> of an optimization problem. Such functions are used to replace inequality <a href="/facts/Constraint_(mathematics)/QLFIFlFX">constraints</a> 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.
</p><p>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 <a href="/facts/Interior_point_method/prIIrceN">interior point methods</a>.
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Barrier function open-in-new

Barrier function