Zero placeholders

! XNLP example demonstrating local optimality and the role of placeholders
!
! This examples solves a simple, then a complex function with many
! local optimal solutions both with SLP and Knitro to demonstrate
! the role of placeholders and delta_z, which while allows SLP to
! make long steps in degenrate situations, also tends to drive it to 
! solutions with a large vertex index.
!
! 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) 2013-2024 Fair Isaac Corporation
!       author: Zsolt Csizmadia
model mmxnlp_nlp_duals
uses "mmxnlp"; 

declarations
 x: mpvar
end-declarations

x is_free
-1 <= x
      x <= 1

!setparam("xnlp_verbose",1)

! Start solving using a second order method, startign from 0, 1, and -1
setparam("xnlp_solver",XNLP_SOLVER_KNITRO)
setparam("XPRS_NLPSOLVER",1)
setinitval(x,0)
minimize(x^3)
Knitro_zero := getobjval
Knitro_zero_x := getsol(x)


setinitval(x,1)
minimize(x^3)
Knitro_one := getobjval
Knitro_one_x := getsol(x)

setinitval(x,-1)
minimize(x^3)
Knitro_mone := getobjval
Knitro_mone_x := getsol(x)

! Now solve using SLP
setparam("xnlp_solver",XNLP_SOLVER_XSLP)
setinitval(x,0)
minimize(x^3)
SLP_zero := getobjval
SLP_zero_x := getsol(x)

setinitval(x,1)
minimize(x^3)
SLP_one := getobjval
SLP_one_x := getsol(x)

setinitval(x,-1)
minimize(x^3)
SLP_mone := getobjval
SLP_mone_x := getsol(x)

! Summarize
writeln
writeln("Function: x^3")
writeln("Starting point:     -1            0            1   ");
writeln("---------------------------------------------------")
writeln("Knitro : ",strfmt(Knitro_mone,13), strfmt(Knitro_zero,13), 
        strfmt(Knitro_one,13));
writeln("SLP    : ",strfmt(SLP_mone,13), strfmt(SLP_zero,13), strfmt(SLP_one,13));
writeln("-- at x = ")
writeln("Knitro : ",strfmt(Knitro_mone_x,13), strfmt(Knitro_zero_x,13), 
        strfmt(Knitro_one_x,13));
writeln("SLP    : ",strfmt(SLP_mone_x,13), strfmt(SLP_zero_x,13), 
        strfmt(SLP_one_x,13));

objective := x*sin((10*x)^2);

! Start solving using a second order method, startign from 0, 1, and -1
setparam("xnlp_solver",XNLP_SOLVER_KNITRO)
setinitval(x,0)
minimize( objective )
F_Knitro_zero := getobjval
F_Knitro_zero_x := getsol(x)

setinitval(x,1)
minimize( objective )
F_Knitro_one := getobjval
F_Knitro_one_x := getsol(x)

setinitval(x,-1)
minimize( objective )
F_Knitro_mone := getobjval
F_Knitro_mone_x := getsol(x)

! Now solve using SLP
setparam("xnlp_solver",XNLP_SOLVER_XSLP)
setinitval(x,0)
minimize( objective )
F_SLP_zero := getobjval
F_SLP_zero_x := getsol(x)

setinitval(x,1)
minimize( objective )
F_SLP_one := getobjval
F_SLP_one_x := getsol(x)

setinitval(x,-1)
minimize( objective )
F_SLP_mone := getobjval
F_SLP_mone_x := getsol(x)

! Summarize
writeln
writeln("Function: x*sin((10*x)^2)")
writeln("Starting point:     -1            0            1   ");
writeln("---------------------------------------------------")
writeln("Knitro : ",strfmt(F_Knitro_mone,13), strfmt(F_Knitro_zero,13), 
        strfmt(F_Knitro_one,13));
writeln("SLP    : ",strfmt(F_SLP_mone,13), strfmt(F_SLP_zero,13),
        strfmt(F_SLP_one,13));
writeln("-- at x = ")
writeln("Knitro : ",strfmt(F_Knitro_mone_x,13), strfmt(F_Knitro_zero_x,13), 
        strfmt(F_Knitro_one_x,13));
writeln("SLP    : ",strfmt(F_SLP_mone_x,13), strfmt(F_SLP_zero_x,13), 
        strfmt(F_SLP_one_x,13));
end-model

end-model