In constrained optimization

Optimization (mathematics)

In mathematics, computational science, or management science, mathematical optimization refers to the selection of a best element from some set of available alternatives....

, a field of mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, a barrier function is a continuous function

Continuous function

In mathematics, a continuous function is a function for which, intuitively, "small" changes in the input result in "small" changes in the output. Otherwise, a function is said to be "discontinuous". A continuous function with a continuous inverse function is called "bicontinuous".Continuity of...

 whose value on a point increases to infinity as the point approaches the boundary of the feasible region

Candidate solution

In optimization , a candidate solution is a member of a set of possible solutions to a given problem. A candidate solution does not have to be a likely or reasonable solution to the problem – it is simply in the set that satisfies all constraints.The space of all candidate solutions is called the...

 (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 to logarithmic barrier function was motivated by its connection with primal-dual interior point method

Interior point method

Interior point methods are a certain class of algorithms to solve linear and nonlinear convex optimization problems.The interior point method was invented by John von Neumann...

.