Optimization: principles and algorithms, by Michel Bierlaire
Functions
longSteps.m File Reference

Algorithm 18.4: long steps interior point algorithm. More...

Go to the source code of this file.

Functions

function longSteps (in A, in b, in c, in x0, in lambda0, in mu0, in eps, in gamma)
 Applies the long step interior point algorithm to solve

\[\min_x c^Tx \]

subject to

\[Ax = b\]

and

\[ x \geq 0 \]

. More...

 

Detailed Description

Algorithm 18.4: long steps interior point algorithm.

Implementation of algorithm 18.4 of [1]

Note
Tested with run1807longSteps.m
Author
Michel Bierlaire
Date
Mon Mar 23 14:52:36 2015

Definition in file longSteps.m.

Function Documentation

function longSteps ( in  A,
in  b,
in  c,
in  x0,
in  lambda0,
in  mu0,
in  eps,
in  gamma 
)

Applies the long step interior point algorithm 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 primal point (nx1)
lambda0starting dual point for equality constraints (mx1)
mu0starting dual point for inequality constraints (nx1)
epsalgorithm stops if $\|d_k\| \leq \varepsilon $.
gammaparameter such that gamma > 0 (default: 1.0e-3)
sigmaparameter such that 0 < sigma < 1 (default: 0.1)
maxitermaximum number of iterations (default: 100)
Returns
[x,lambda,mu]
x: primal solution
lambda: dual solution for equality constraints
mu: dual solution for inequality constraints
Copyright 2015-2016 Michel Bierlaire