An infeasible primal-dual path-following Interior Point Method (IPM) with controlled perturbations for Linear Programming (LP). The use of controlled perturbations improves active-set prediction capabilities of IPMs for LP.
!!!Before Start!!!
In Unix, add the /path/to/thirdParty/lp_solve/src to LD_LIBRARY_PATH
In Windows, add the \path\to\thirdParty\lp_solve\bin\win64 to system environment variable PATH
The main solver PIPM (/src/pipm.m) only accepts LP problems in the standard form, i,e,
min c'*x s.t. Ax = b, x>=0.
The future version may also accept QP problems, but currently it has not been implemented.
Syntax:
p = pipm( A, b, c); p.solve;
p = pipm( A, b, c, options); p.solve;
Input:
(A,b,c) - problem data
options - struct, optional input, controlling all parameters
.maxIter Maximum number of iterations allowed
Default value 100
.tol Convergence tolerance
Default value 1e-06
.mu_cap Threshold value for mu
Default value 1e-03
.cutoff Threshold value for cutoff
Default value 1e-05
.iPer Initial perturbations
Default value 1e-02
.actvPredStrtgy Active-set prediction strategy
Default value 'conservCutoff'
'conservCutoff' - cutoff
'conservIdFunc' - identification function
'conservIndica' - indicators
.doCrossOver Controls whether or not perform crossover to
simplex after ipm iterations.
Default value 1
0 - No
1 - Yes
.verbose Controls how much information to display.
Default value 2
0 - Nothing
1 - Only optimal information
2 - Iterative information
>=3 - All information
PIPM as normal infeasible primal-dual path-following IPM:
options.iPer = 0; % No perturbations
options.doCrossOver = 0; % Disable crossover to simplex
options.mu_cap = 1e-09; % Push duality gap to sufficiently small
p = pipm( A, b, c, options);
p.solve;
Example:
Please see examples.m in folder Examples
Author:
Yiming Yan @ University of Edinburgh
Reference:
Coralia Cartis and Yiming Yan, Active-set prediction for interior point methods using controlled perturbations, submitted, April 2014
Have Fun! :)
Yiming Yan, University of Edinburgh
April 15, 2014
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