Interior point method

（重定向自Barrier method）

The graph of a strictly concave quadratic function is shown in blue, with its unique maximum shown as a red dot. Below the graph appears the contours of the function: The level sets are nested ellipses.

Interior point methods (also referred to as barrier methods) are a certain class of algorithms that solves linear and nonlinear convex optimization problems.

John von Neumann suggested an interior point method of linear programming which was neither a polynomial time method nor an efficient method in practice. In fact, it turned out to be slower in practice compared to simplex method which is not a polynomial time method. In 1984, Narendra Karmarkar developed a method for linear programming called Karmarkar's algorithm which runs in provably polynomial time and is also very efficient in practice. It enabled solutions of linear programming problems which were beyond the capabilities of the simplex method. Contrary to the simplex method, it reaches a best solution by traversing the interior of the feasible region. The method can be generalized to convex programming based on a self-concordant barrier function used to encode the convex set.

单词	Barrier method
释义	Barrier method 原声例句 TED-Ed（视频版） These contraceptives are sometimes called barrier methods and can be used with spermicides, an example of the second category, disable. 这些避孕药有时被称为屏障方法，可以与杀精子剂一起使用，第二类的一个例子是禁用。英语百科 Interior point method （重定向自Barrier method） Interior point methods (also referred to as barrier methods) are a certain class of algorithms that solves linear and nonlinear convex optimization problems. John von Neumann suggested an interior point method of linear programming which was neither a polynomial time method nor an efficient method in practice. In fact, it turned out to be slower in practice compared to simplex method which is not a polynomial time method. In 1984, Narendra Karmarkar developed a method for linear programming called Karmarkar's algorithm which runs in provably polynomial time and is also very efficient in practice. It enabled solutions of linear programming problems which were beyond the capabilities of the simplex method. Contrary to the simplex method, it reaches a best solution by traversing the interior of the feasible region. The method can be generalized to convex programming based on a self-concordant barrier function used to encode the convex set.
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