the solutions of many linear programs min c.x under A x = y, x >= 0 at once, each the analytic centre of its optimal face; MATLAB’s linprogCentre

Syntax

x = linprogCentre(c, A, y)

One program.

x = linprogCentre(C, A, Y)

One program per row of C and Y.

x = linprogCentre(c, A, y, tol=1e-6, maxIter=20)

A coarser stop.

Description

Where the optimum is not unique the solution is the centre of the optimal face, which is symmetric where the program is, where a simplex gives any vertex of it; this is the choice of the shears in the Taylor model. The programs are solved together by a primal dual path following method, its Newton steps aimed at the central path at 0.3 mu.

Input

c (n,) or (N, n), the costs
A (m, n) or (N, m, n), the constraint matrix
y (m,) or (N, m), the right hand sides

Keywords

keyword default description
tol 1e-09 the relative tolerance of the primal and dual residuals and the duality gap
maxIter 100 the largest number of Newton steps

Output

x (n,) or (N, n), the solutions; NaN for a program that does not converge

See also

linearProgram, calcTaylor, TaylorModel

MATLAB’s linprogCentre

source

Citing this page. This page is part of the documentation of MTEX, a free and open source MATLAB toolbox for analyzing and modeling crystallographic textures. It was written by The MTEX Developers and is published at https://mtex-toolbox.github.io/linprogCentre_py.html. If you use MTEX, or reuse text or figures from this page, in your research, please cite

F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63

BibTeX 
@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}

Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.