In constrained
optimizationIn mathematics, optimization, or mathematical programming, refers to choosing the best element from some set of available alternatives.In the simplest case, this means solving problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or...
, a field of
mathematicsMathematics is the science and study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions....
, a
barrier function is a
continuous functionIn 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...
whose value on a point increases to infinity as the point approaches the boundary of the
feasible regionIn 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...
(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.
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In constrained
optimizationIn mathematics, optimization, or mathematical programming, refers to choosing the best element from some set of available alternatives.In the simplest case, this means solving problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or...
, a field of
mathematicsMathematics is the science and study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions....
, a
barrier function is a
continuous functionIn 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...
whose value on a point increases to infinity as the point approaches the boundary of the
feasible regionIn 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...
(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.