[Ipopt] ipopt with l-bfgs: slow progress on unbounded linear objective

Ipopt User ipoptuser at gmail.com
Thu Jun 18 11:49:21 EDT 2015

When I try to solve the simple scalar problem min{-x : x >= 0} with IPOPT
and use hessian_approximation = limited-memory, the progress is very slow.
Essentially, x is reduced by 1 in each iteration.

>From what I understand, this is due to the Hessian approximation, which in
this case is just the identity matrix (plus 1/x due to the log barrier
term, which is significant only in the first few iterations). Solving Hs =
-g, with H the Hessian, s the step and g the gradient, it finds s = 1.
Indeed when I set limited_memory_init_val = 0.1, x is reduced by 10 in each

This seems undesirable to me. Other L-BFGS based solvers like SNOPT and
L-BFGS-B figure out that the problem is unbounded in a few iterations.
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