### tp040r.apm.m4

Model tp040r
! 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 the solution becomes unique.
ifdef(`revisedhs',`define(`stricths',0)',`define(`stricths',1)')
Parameters
lbx3 = 0
End Parameters
Variables
x[1] = 0.8
x[2] = 0.8
x[3] = 0.8 ifelse(stricths,1,`',`, >= lbx3')
x[4] = 0.8
obj
End Variables
Equations
x[1]^3 + x[2]^2 - 1 = 0
x[1]^2*x[4] - x[3] = 0
x[4]^2 - x[2] = 0
obj = -x[1]*x[2]*x[3]*x[4]
! best known objective = -0.25
! begin of best known solution belonging to the revised case
! x[1] = 2^(-1/3) = 0.7937005259840997
! x[2] = 2^(-1/2) = 0.7071067811865475
! x[3] = 2^(-11/12) = 0.5297315471796476
! x[4] = 2^(-1/4) = 0.8408964152537145
! end of best known solution belonging to the revised case
End Equations
End Model

Stephan K.H. Seidl