Camar algorithm

Basic introduction

1984, Indian mathematician N.karmark proposed a new polynomial time algorithm for linear planning issues, in terms of actual computational efficiency, showing it The huge potential of single-form method competition, the Karmarkar algorithm is proposed by linear planning theory research, and the powerful vitality and broad application prospects are also shown to handle nonlinear optimization.

Single method is to solve the (LP) problem by examining the method of the linear domain boundary, and the Karmarkar algorithm is built on the single-shaped structure, the algorithm starts from the initial internal point, Along the most flexible direction, the Karmark algorithm is also referred to as an intact method, so that the Karmarkar algorithm is also known as the internal point method, so for large-scale linear planning issues, when constrained conditions and variables When the number increases, the number of iterations of the inner point algorithm has changed less, and the convergence and calculation speed are better than the simple form.

Camar algorithm considers the following standard forms of linear planning issues

Meet

and

or

Here is the N-dimensional vector of the total component of 1, and is known:

1.

;

2.

;

3. For a given accuracy

, when you can solve

When you meet the condition

, it will stop iteration, and it is considered to be the solution of X is the solution.

Camar algorithm step

The Camar algorithm step is as follows:

1. (initial) set K = 0,

is a N-dimensional vector with a component of 1 / n.

2. (determined) If

stops iteration, the optimal solution is

3 . With x component is a diagonal element, do diagonal array

set

here E is all components 1 Vector 2N dimension vector.

4. (Projection Transformation) to

, set

,

/ p>

5. Set

.

6. Set

, where α is constant that satisfies

, usually

.

7.