### tp033r.apm.m4

Model tp033r
! Source version 1
! The present file has to be drawn through the m4 macro processor
! at first, with or without `-Drevisedhs'. With the macro
! defined, the feasible domain is reduced in comparison with the H+S
! one such that some unwanted secondary minimum is excluded.
ifdef(`revisedhs',`define(`stricths',0)',`define(`stricths',1)')
Parameters
lbx2hs = 0
lbx2r = 10^(-5)
lbx2 = ifelse(stricths,1,`lbx2hs',`lbx2r')
End Parameters
Variables
x[1] = 0, >= 0
x[2] = lbx2, >= lbx2
x[3] = 3, >= 0, <= 5
obj
End Variables
Equations
x[3]^2 - x[2]^2 - x[1]^2 >= 0
x[1]^2 + x[2]^2 + x[3]^2 - 4 >= 0
obj = (x[1] - 1)*(x[1] - 2)*(x[1] - 3) + x[3]
! best known objective = sqrt(2) - 6 = -4.585786437626905
! begin of best known solution belonging to the revised case
! x[1] = 0
! x[2] = sqrt(2) = 1.414213562373095
! x[3] = sqrt(2) = 1.414213562373095
! end of best known solution belonging to the revised case
End Equations
End Model

Stephan K.H. Seidl