[Ipopt] Bound-constrained solution worst than initial guess

[Peter Carbonetto]

> I've found a solution for my problem by adjusting the value of the
> option bound_mult_init_val from 1 to 0.001.

That's interesting. What you did was initialize the Lagrange multipliers 
corresponding to the bound constraints. What this means is that you've 
found a good initial candidate for the Lagrange multipliers, so that it is 
closer to satisfying the optimality conditions (inf_pr and inf_du in the 
output). I believe it is possible to output the values of the Lagrange 
multipliers at the solution (depending on what interface you are using) 
and you might find that the Lagrange multipliers at the solution are close 
to the ones you chose.

You might also find that setting the initial value of the barrier 
parameter (mu) to a small number works, too.

Peter Carbonetto
Ph.D. Candidate
Dept. of Computer Science
University of British Columbia