[Ipopt] Question about the too many iteration in Ipopt

[Run Zhu]

Dear All,

I am PhD student of Northeastern University, specializing in computational
material science. My current work is to determine the equilibrium position
of dislocation in the metal bar under tensile load. This is achieved by
minimizing interaction energy of dislocation. The optimization model, for a
single degree of freedom, is

find: x
min: W = - ln ( x^2 + a^2) - b*x
st: lb < x < ub

where optimization variable, x, is the position of dislocation; objective
function, W, is the interaction energy; a and b are constant, and lb and ub
are the upper and lower bound. The attached figure shows the x versus W.
The boundary is also considered.

The initial value x0 is the equilibrium position in last loading step,
which is pretty close to the optimal x*

The ipopt works perfectly well when the number of degree of freedom is low,
like 50. However, when the no. of optimization variable, x, is greater than
100, ipopt takes many search around x*, up to 500 times. The gradient is
analytically available for this problem and the minimum is always there.
But I cannot figure out how this happens.

If you have any idea to this situation. Please feel free to contact me so
that I can provide more details.

Thanks

Cheers

Run Zhu


-- 
Run Zhu, PhD student
Department of Mechanical and Industrial Engineering
Northeastern University
Boston, MA 02115
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