In constrained optimization, a field of mathematics, a barrier function is a continuous function whose value on a point increases to infinity as the point approaches the boundary of the feasible region (Nocedal and Wright 1999). It is used as a penalizing term for violations of constraints. The two most common types of barrier functions are inverse barrier functions and logarithmic barrier functions. Resumption of interest in logarithmic barrier function was motivated by its connection with primal-dual interior point method.
When optimising a function f(x), the variable can be constrained to be strictly lower than some constant by instead optimising the function . Here, is the barrier function.
Read more about Barrier Function: Logarithmic Barrier Function
Famous quotes containing the words barrier and/or function:
“The hearts of Afro-American women are too warm and too large for race hatred. Long suffering has so chastened them that they are developing a special sense of sympathy for all who suffer and fail of justice.”
—Fannie Barrier Williams (1855–1944)
“The fact remains that the human being in early childhood learns to consider one or the other aspect of bodily function as evil, shameful, or unsafe. There is not a culture which does not use a combination of these devils to develop, by way of counterpoint, its own style of faith, pride, certainty, and initiative.”
—Erik H. Erikson (1904–1994)