Weight on Linear Objective

Type

Floating point number

Range

[0,1e20]

Default

0

This option invokes the so-called composite objective technique, if the first solution obtained is infeasible, and if the objective function contains linear terms. While trying to reduce the sum of infeasibilities, the method also attempts to optimize the linear objective.

At each infeasible iteration, the objective function is defined to be

minimize sw(cTx) + (sum of infeasibilities),

where s = 1 for minimization, s = -1 for maximization, and c is the linear objective.

If an “optimal” solution is reached while still infeasible, w is reduced by a factor of 10. This helps to allow for the possibility that the initial w is too large. It also provides dynamic allowance for the fact that the sum of infeasibilities is tending towards zero.

The effect of w is disabled after 5 such reductions, or if a feasible solution is obtained.