### tp020r.apm.m4

Model tp020r
! 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
lbx1hs = -1/2
lbx1r = 0
lbx1 = ifelse(stricths,1,`lbx1hs',`lbx1r')
End Parameters
Variables
x[1] = -2, >= lbx1, <= 1/2
x[2] = 1
obj
End Variables
Equations
x[1] + x[2]^2 >= 0
x[1]^2 + x[2] >= 0
x[1]^2 + x[2]^2 - 1 >= 0
obj = 100*(x[2] - x[1]^2)^2 + (1 - x[1])^2
! best known objective = 81.5 - 25*sqrt(3) = 38.19872981077807
! begin of best known solution belonging to the revised case
! x[1] = 0.5
! x[2] = sqrt(3)/2 = 0.8660254037844386
! end of best known solution belonging to the revised case
End Equations
End Model

Stephan K.H. Seidl