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Local solutions

Description
Nonlinear example demonstrating the presence of locally optimal solutions, and the role of initial points

Further explanation of this example: 'Xpress NonLinear Reference Manual'

Source Files
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xnlp_local_optima.mos

! XNLP example demonstrating the presence of locally optimal solutions, and the
! role of initial points
!
! This example performs a series of solves for the exact same problem having
! several local optimas
!
! This example demonstrates a particular non-linear optimization concept as related
! to Xpress NonLinear.
! The version of the example is for Xpress 7.5.
!
!  (c) 2013 Fair Isaac Corporation
model mmxnlp_nlp_duals
uses "mmxnlp";

declarations
x,y: mpvar
end-declarations

!setparam("xnlp_verbose",1)

! A function with several local valleys
x^2*sin(x) >= y

! Observe the regions of attractions
writeln("Locally optimal solutions found:")
writeln("------------------------------------------")
writeln("        x            y         objective  ")
writeln("------------------------------------------")
forall (i in -5..40) do
setinitval(x,i)
setinitval(y,i)
minimize(x+y)
if (getparam("xnlp_nlpstatus") = XNLP_STATUS_LOCALLY_OPTIMAL) then
writeln(strfmt(getsol(x),13),",",strfmt(getsol(y),13),": ",
strfmt(getobjval,13))
else
writeln("Status is not locally optimal")
end-if
end-do

end-model