Barrier Function
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.
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- Example(s):
- See: Interior Point Algorithm, Candidate Solution.
References
2014
- http://en.wikipedia.org/wiki/Barrier_function
- 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 functions was motivated by their connection with primal-dual interior point method.
When optimizing a function f(x), the variable [math]\displaystyle{ x }[/math] can be constrained to be strictly lower than some constant [math]\displaystyle{ b }[/math] by instead optimizing the function [math]\displaystyle{ f(x) + g(x,b) }[/math]. Here, [math]\displaystyle{ g(x,b) }[/math] is the barrier function.
- 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 functions was motivated by their connection with primal-dual interior point method.
1999
- (Nocedal & Wright 1999) ⇒ Jorge Nocedal, and Stephen Wright. (1999). “Numerical Optimization.” ISBN 0-387-98793-2.