A barrier function penalizes approaching the boundary of a feasible set from its interior, typically diverging to there. An interior-point method minimizes the original objective function plus a positive multiple of this penalty, then reduces that multiple. The logarithmic barrier is the basic example for smooth inequality optimization constraints.
A barrier function is a concept commonly used in optimization, particularly in the context of constrained optimization problems. Barrier functions help to modify the optimization problem so that the constraints are incorporated into the objective function, allowing for easier handling of constraints during the optimization process. The main idea is to add a penalty to the objective function that becomes increasingly large as the solution approaches the boundaries of the feasible region defined by the constraints.
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