S.U.Ngueveu.Web

# Sandra U. NGUEVEU

Maître de Conférences / Associate Professor

 Summary Publications ResearchProjects Service PhD HDR Software Teaching C.V.(28.01.2019)

• JULIA package LinA

• NEW !!!! Link to github : https://github.com/LICO-labs/LinA.jl :

• How to cite : if you find LinA useful, please cite as follows : Julien Codsi, Sandra Ulrich Ngueveu and Bernard Gendron (2021). LinA: A faster approach to piecewise linear approximations using corridors and its application to mixed-integer optimization. LAAS report n° 21221, hal-03336003.

• How to import the LinA package in julia:

or from the package manager of julia: add https://github.com/LICO-labs/LinA.jl.git

• How to use (examples)

• using LinA
expr1=:((sqrt(x))*(sin(x))+x)
pwl = Linearize(expr1, 1, 5, Absolute(0.32))
pwl = Linearize(expr1, 1, 5, Relative(0.32))
pwl = Linearize(expr1, 1, 5, Absolute(0.32), HeuristicLin())
pwl = Linearize(expr1, 1, 5, Absolute(0.32), ExactLin())
pwl = Linearize(expr1, 1, 5, Absolute(0.32), HeuristicLin(); ConcavityChanges=[3.4203854894568733] )
pwl = Linearize(expr1, 1, 5, Absolute(0.32), ExactLin(); ConcavityChanges=[3.4203854894568733] )
pwl = Linearize(expr1, 1, 5, Relative(0.32); bounding = Under())
pwl = Linearize(expr1, 1, 5, Relative(0.32); bounding = Over())
pwl = Linearize(expr1, 1, 5, Relative(0.32); bounding = Best())

origf = x->sin(x)/x
begx=1
endx=12
deltax=0.01
pwl = Linearize(origf, begx, endx, Absolute(deltax))
pwl = Linearize(origf, begx, endx, Absolute(deltax), ExactLin())
...

• The output

• pwl is an array of linear functions
Each linear piece is characterized with: xMin, xMax, a, b, fct

• Plotting the output

• using Plots
thefig = plot(origf, begx, endx, label="sin(x)/x", title="ExactLin()")
for i in 1:length(pwl)
thefig=plot!(x->pwl[i](x), pwl[i].xMin, pwl[i].xMax, label="pwl_p"*string(i));
end
@show thefig

• Related talks (these are talks without proceedings, please see section "how to cite" above to access the paper; If you find LinA useful, please cite the reference to that paper)

• Piecewise linear approximation with a performance guarantee for solving MINLPs .
Journées de l'optimisation (JOPT), Mai 2019, HEC Montréal, Canada.
speaker : J. Codsi

• Mixed Integer Optimization Using Piecewise Linear Function Fitting and JULIA-based library.
PGMO Days 2019, December 2019, Paris, France.
speaker : S.U. Ngueveu

• Non necessarily continuous piecewise linear approximation with a performance guarantee : application to mixed integer optimization .
ROADEF 2020, February 2020, Montpellier, France.
speaker : S.U. Ngueveu

• LinA: an opensource Julia-based package for piecewise linear approximation of continuous univariate functions with (dis-)continuous piecewise linear functions .
ROADEF 2021, April 2021, Mulhouse (online), France.
speaker : S.U. Ngueveu

• Acknowledgments

• This research benefited from the support of the FMJH Program PGMO and from the support to this program from EDF-Thales-Orange.
This research benefited from the support of the SMI program of Toulouse INP and from the Undergraduate Student Research Awards from NSERC.