Optimization: principles and algorithms, by Michel Bierlaire
Functions

Algorithm 17.3: Dikin's method. More...

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Functions

function dikin (in A, in b, in c, in x0, in eps, in beta)
 Applies Dikin's method to solve

\[\min_x c^Tx \]

subject to

\[Ax = b\]

and

\[ x \geq 0 \]

. More...

 

Detailed Description

Algorithm 17.3: Dikin's method.

Implementation of algorithm 17.3 of [1]

Note
Tested with run1703.m
Tested with run1607dikin.m
Author
Michel Bierlaire
Date
Sun Mar 22 16:39:13 2015

Definition in file dikin.m.

Function Documentation

function dikin ( in  A,
in  b,
in  c,
in  x0,
in  eps,
in  beta 
)

Applies Dikin's method to solve

\[\min_x c^Tx \]

subject to

\[Ax = b\]

and

\[ x \geq 0 \]

.

Parameters
Athe constraint matrix
bthe constraint right hand side
cthe cost vector for the objective function
x0starting point
epsalgorithm stops if $\|d_k\| \leq \varepsilon $.
betaparameter such that 0 < beta < 1 (default: 0.9)
maxitermaximum number of iterations (default: 100)
Returns
[solution,iteres,niter]
solution: local minimum of the function
iteres: sequence of iterates generated by the algorithm. It contains n+2 columns. Columns 1:n contains the value of the current iterate. Column n+1 contains the value of the objective function. Column n+2 contains the value of the norm of the gradient. It contains maxiter rows, but only the first niter rows are meaningful.
unbounded If 0, the problem is unbounded. If different from 0 the problem is bounded.
Copyright 2015-2016 Michel Bierlaire