GAMS — The Solver Manuals - Available Software

340 MINOS
obj.. z =e= sum(i, sqr(resid(i)));
model m /all/;
solve m using nlp minimizing z;
This can be cast in form NLP (equations (1) − (4)) by saying minimize z subject to z = ∑ i resid2 i and the other
constraints in the model. Although simple, this approach is not always preferable. Especially when all constraints
are linear it is important to minimize ∑ i resid2 i directly. This can be achieved by a simple reformulation: z can
be substituted out. The substitution mechanism carries out the formulation if all of the following conditions hold:
• the objective variable z is a free continuous variable (no bounds are defined on z),
• z appears linearly in the objective function,
• the objective function is formulated as an equality constraint,
• z is only present in the objective function and not in other constraints.
For many models it is very important that the nonlinear objective function be used by MINOS. For instance the
model chem.gms from the model library solves in 21 iterations. When we add the bound
energy.lo = 0;
on the objective variable energy and thus preventing it from being substituted out, MINOS will not be able to
find a feasible point for the given starting point.
This reformulation mechanism has been extended for substitutions along the diagonal. For example, the GAMS
model
variables x,y,z;
equations e1,e2;
e1..z =e= y;
e2..y =e= sqr(1+x);
model m /all/;
option nlp=minos;
solve m using nlp minimizing z;
will be reformulated as an unconstrained optimization problem
minimize f(x) = (1 + x) 2 .
These additional reformulations can be turned off by using the statement option reform = 0; (see §4.1).
5 GAMS Options
The following GAMS options are used by GAMS/MINOS:
5.1 Options Specified through the Option Statement
The following options are specified through the option statement. For example,
option iterlim = 100 ;
sets the iteration limit to 100.