(!*********************************************************************
Mosel NL examples
=================
file catenary.mos
`````````````````
QCQP problem (linear objective, convex quadratic constraints)
Based on AMPL model catenary.mod
(Source: http://www.orfe.princeton.edu/~rvdb/ampl/nlmodels/ )
This model finds the shape of a hanging chain by
minimizing its potential energy.
(c) 2008 Fair Issac Corporation
author: S. Heipcke, May 2008
*********************************************************************!)
model "catenary"
uses "mmxprs", "mmnl"
parameters
N = 100 ! Number of chainlinks
L = 1 ! Difference in x-coordinates of endlinks
H = 2*L/N ! Length of each link
end-parameters
declarations
RN = 0..N
x: array(RN) of mpvar ! x-coordinates of endpoints of chainlinks
y: array(RN) of mpvar ! y-coordinates of endpoints of chainlinks
end-declarations
forall(i in RN) x(i) is_free
forall(i in RN) y(i) is_free
! Objective: minimise the potential energy
potential_energy:= sum(j in 1..N) (y(j-1)+y(j))/2
! Bounds: positions of endpoints
! Left anchor
x(0) = 0; y(0) = 0
! Right anchor
x(N) = L; y(N) = 0
! Constraints: positions of chainlinks
forall(j in 1..N)
Link(j):= (x(j)-x(j-1))^2+(y(j)-y(j-1))^2 <= H^2
! Setting start values
forall(j in RN) setinitval(x(j), j*L/N)
forall(j in RN) setinitval(y(j), 0)
(! For exporting the matrix file
setparam("XPRS_loadnames", true)
loadprob(potential_energy)
writeprob("catenary.mat","l")
!)
setparam("XPRS_verbose", true)
minimise(potential_energy)
writeln("Solution: ", getobjval)
forall(j in RN)
writeln(strfmt(getsol(x(j)),10,5), " ", strfmt(getsol(y(j)),10,5))
end-model
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