Solving a nonlinear equation system

Engineers often wish to solve a nonlinear system of equations often in a chemical equilibrium or oil refining context.  Many such problem types exist.  A simple form of one follows as adapted from the GAMS model library and the paper Wall, T W, Greening, D, and Woolsey , R E D, "Solving Complex Chemical Equilibria Using a Geometric-Programming Based Technique". Operations Research 34, 3 (1987). which is

ba * so4 = 1

baoh / ba / oh = 4.8

hso4 / so4 / h =0 .98

h * oh = 1

ba + 1e-7*baoh = so4 + 1e-5*hso4

2 * ba + 1e-7*baoh + 1e-2*h = 2 * so4 + 1e-5*hso4 + 1e-2*oh

which is a nonlinear system of equations where the variables are ba, so4, baoh, oh, hso4 and h.  The simplest GAMS formulation of this is (nonlinsys.gms)

Variables ba, so4, baoh, oh, hso4, h ;

Equations r1, r2, r3, r4, b1, b2 ;

r1..  ba * so4 =e= 1 ;

r2..  baoh / ba / oh =e= 4.8 ;

r3..  hso4 / so4 / h =e= .98 ;

r4..  h * oh =e= 1 ;

b1..  ba + 1e-7*baoh =e= so4 + 1e-5*hso4 ;

b2..  2 * ba + 1e-7*baoh + 1e-2*h =e= 2 * so4 + 1e-5*hso4 + 1e-2*oh ;

Model wall / all / ;

ba.l=1; so4.l=1; baoh.l=1; oh.l=1; hso4.l=1; h.l=1;

Solve wall using nlp minimizing ba;